## Шевчук Ігор Олександрович

Професор кафедри, член-кореспондент НАН України, професор, доктор фізико-математичних наук

Curriculum Vitae

Taras Shevchenko National University of Kyiv (Kyiv University),

Faculty of Mechanics and Mathematics,

60 Volodymyrska Street,

01033 Kyiv, Ukraine

Phone: (380-44) 521-33-67

Fax: (380-44) 259-07-85

E-mail: shevchukh@ukr.net

Date/Place of Birth: 29 April 1947, Kyiv, Ukraine

Education:

Kyiv University, Student, 1964 — 1969

Institute of Mathematics National Academy of Sciences of Ukraine (IM for later references),

Post graduate student, 1969 — 1972, supervisor Professor V. K. Dzjadyk

Ph.D. (Phys. & Math. Sc.), IM, 1973

Dissertation Title: On Plemelj-Privalov theorem and constructive characteristic of functions of

Zygmund class

Doctor of Sciences (Phys. & Math.), IM, 1985

Dissertation Title: Extension and approximation of smooth functions of one variable

Primary Fields of Interest According to the AMS Classification:

Approximations and expansions (41)

Sequences, series, summability (40)

Functions of complex variable (30)

Numerical analysis (65)

Finite differences and functional equations (39)

Experience:

1972 – 1977 Junior Scientist, IM .

1977 – 1979 Science secretary of the IM.

1979 – 1986 Senior Scientist, IM .

1986 – 1998 Providing Scientist, IM.

1998 – present Chair of the department of Mathematical analysis, Taras Shevchenko National

University of Kyiv.

1986 – present Professor(1/4 position), National Pedagogical University.

Teaching Experience:

mathematical analysis, complex analysis, real analysis, functional analysis, differential equati-

ons, approximation theory, elements of numerical analysis.

1

Conferences

(1) School on Function’s theory, July 1969, Makhachkala, Russia

(2) School on Approximation theory, June 1974, Agveran, Armenia

(3) Int. Conf. The theory of approximation of functions July 1975, Kaluga, Russia

(4) All-Union Simposium on the approximation theory in the complex domain, May 1976,

Upha, Russia

(5) Int. Conf. Constructive function theory, May 1977, Blagoevgrad, Bulgaria

(6) School Approximation theory, June 1978, Yalta, Ukraine

(7) Conference on analytic functions, Kozubnik, Poland, April 18-26, 1979.

(8) Int. Conf. Approximation and function spaces, August 1979, Gdansk, Poland

(9) School Complex analysis, June 1981, Yalta, Ukraine

(10) Int. Conf. The theory of approximation of functions, May, 1983, Kyiv, Ukraine

(11) Int. Congress of Math., August 1983, Warsaw, Poland

(12) Int. Conf. Constructive function theory, May 1984, Varna, Bulgaria (was not allowed to

go, but the abstract is published)

(13) Stechkin’s school on function’s theory, July 1984, Miass, Russia

(14) Conf. on function’s theory, dedicated to S.M.Nikolskii’s 80-th anniversary, April 1985,

Dnepropetrovsk, Ukraine

(15) Saratov winter school on function’s theory, February 1988, Russia

(16) Conf. on function’s theory, dedicated to V.K.Dzjadyk’s 70-th anniversary, August 1989,

Lutsk, Ukraine

(17) Rasshirennye zasedanija seminara instituta prikladnoj matematiki im. I.N.Vekua, Tbi-

lisi, 23-26.04.1990.

(18) Conf. Extremal problems of approximation theory and their appl., dedicated to N.P.

Korneichuk’s 70-th anniversary, 29-31 May 1990, Kyiv, Ukraine

(19) Int. conf. on approximation theory, Budapest, 5.09-11.09, 1990 (was not able to go, but

the abstract is published)

(20) School on function’s theory, July 1991, Odesa, Ukraine

(21) Saratov winter school on function’s theory, February 1992, Russia

(22) Int. Conf., dedicated to 100-th anniversary of Stefan Banach, May 1992, Lviv, Ukraine

(23) School Fourier series and their applications June 1992, Kamyanets-Podilsky, Ukraine

(24) Int. Conf., dedicated to 100-th anniversary of M.P.Kravchuk, October 1992, Kyiv, Ukrai-

ne

(25) School Theory of functions, differential equantions in mathematical programming, 25

January – 3 February 1993, Voronezh, Russia

(26) School on Potential theory, July 1993, Yalta, Ukraine

(27) Int. Congress EUROSPORE/EURORESEARCH, 3-5 November 1993, Toulon – Var,

France

(28) Saratov winter school on function’s theory, February 1994, Russia

(29) Int. Conf. Third Souslin conference, dedicared to the 100-th anniversary of Michail

Souslin, 20-30 July 1994, Saratov, Russia

(30) Int. Conf. Constructive approximation and its applications, on the ocasion of the reti-

rement of Professor P.Rabinovitz, 17-20 May 1994, Tel Aviv, Israel

(31) XIX Stechkin’s school on function theory, July 1994, Beloretsk, Russia

(32) X Vserossijskaja konferencija “Teoreticheskie osnovy i konstruirovanie chislennyh algori-

tmov reshenija zadach matematicheskoj fiziki posvjashchjennaja pamjati chl.-korr. AN

SSSR K.I.Babenko, 08-12.10.1994, Krasnovidovo (Russia)

(33) Int. Conf. Functional spaces,approximation theory, nonlinear analysis, dedicated to 90-

th anniversary of academician S.M.Nikolskii, April 1995, Moscow, Russia

(34) XX Stechkin’s school on function theory, July 1995, Moscow, Russia

(35) Int. Conf. on Approximation Theory and Function Series, dedicated to Karoly Tandori

on his 70-th birthday, 21-25 August 1995, Budapest, Hungary

(36) Saratov winter school on function’s theory, February 1996, Russia

(37) Int. Conf. on Approximation theory, April 1996, Columbia, USA

(38) Dragoslav S.Mitrinivic Memorial Conference, Belgrad, 20-21.06 1996

(39) Third Int. Conf. Curves and Surfases, 27 June – 3 July 1996, Chamonix Mont Blanc,

France

(40) Int. Conf. Approximation Theory and Numerical Methods, dedicated to 100-th anni-

versary of E.Ya.Remez, 19-21 June 1996, Rivne, Ukraine

(41) ICAOR Int. Conf. on Approximation and Optimization, 29 July – 1 August 1996, Cluj-

Napoca, Romania

(42) XXI Stechkin’s school on function theory, August 1996, Miass, Russia

(43) II school “Fourier series: theory and applications”. Kamyanets-Podilsky 30.06-5.07 1997,

Ukraine (was absent, but the abstract is published)

(44) Int. Colloquium on Applications of Mathematics in memorial Lothar Collats, 4-5 July

1997, Hamburg, Germany

(45) XXII Stechkin’s school on function theory, August 1997, Miass, Russia

(46) Ninth Int. Conf. on Approximation Theory, Nashville, TN, Jan.3 – 6, 1998.

(47) Theory of Approximation of Functions. Colloquium, dedicated to the memory of V.I.Belyi.

Donetsk, 13-15.05 1998.

(48) Approximation methods and orthogonal expansions, Int. Conf., dedicated to 60th bi-

rthday of Gennadi Vainikko, Tartu(Estonia), 29-31.05.1998

(49) Approximation Theory and its Applications. Int. conf. dedicated to the memory of

V.K.Dzjadyk. Ky´ Кv, 27-31.05.1999.

(50) Fourth Int. Conf. Curves and Surfases, 01-07.07. 1999, Saint Malo, France

(51) Int. Colloquium on Applications of Mathematics in memorial Lothar Collats, 1999,

Hamburg, Germany

(52) International conference on Mathematical analysis and economics, Sumy, 19-22.10.1999.

(53) Approximation of functions and operators, Int. conf., dedicated to the 80th birthday of

S.B.Stechkin, Ekaterinburg, 28.02-03.03.2000

(54) Trends in approximation theory, An Int. symposium Celebrating the 60-th birthday of

Larry L. Schumaker, Vanderbilt Univ., Nashville, TN, USA, May 17-20, 2000.

(55) Int. Colloquim on the Applications of Mathematics in memoriam Lothar Collatz (1910

– 1990), Hamburg, September 29 and 30, 2000

(56) Ukrainian Mathem. Congress, dedicated to 200-th anniv. of M.V. Ostrogradsky. Kyiv,

21-23.08 2001

(57) International Conference Functional Methods in Aproximation Theory, Operator Theory,

Stohastic Analysis and Statistics, 15–19.10.2001, Kyiv

(58) Workshop on Approximation Theory, dedicated to 60-th anniv. of D.Leviatan, Tel-Aviv,

Feb. 20-21, 2002

(59) Int. Conf., dedicated to 110-th anniversary of Stefan Banach, May 2002, Lviv, Ukraine

(60) International conference on Mathematical analysis and economics, Sumy, 2003

(61) International Workshop on Analysis and Its Applications, Mersin, Turkey, September ,

07-11, 2004

(62) Approximation and Probability. Conference on the occasion of the 70 anniversary of

Professor Zbigniew Ciesielski, Bedlewo, 20 – 24 September 2004.

(63) International Conference “Functional Methods in Approximation Theory, Operator Theory,

Stochastic Analysis and Statistic II”. October, 1-5, 2004, Kyiv, Ukraine

(64) International Conference “Extremal problems and approximation dedicated to the 70th

birthday of V.M. Tikhomirov, 16-18 December ,Moscow, 2004.

(65) International conference and workshop Functional spaces, Approximation Theory, Nonlnear

Analysis, dedicated to the centennial of Sergei Mikhailovich Nikolskii, Moscow, Russia,

May 23-29, 2005,

(66) VII International Meeting on Approximation Theory of the University of Jaen Ubeda,

Spain, August 31-September 3, 2006.

(67) Mathematical Analysis, Differential Equations and Their Applications, September 18-

23, 2006, Uzhgorod, Ukraine.

(68) CMS-MITACS Joint Conference 2007, May 31- June 3, Winnipeg, Manitoba.

(69) VIII International Meeting on Approximation Theory of the University of Jaen, Ubeda,

Spain, November 7-11, 2007.

(70) Theory of functions and their applications, on occasion of the 70th birthday of academi-

cians A.M. Samoilenko, June 16-21,2008, Melitopol, Ukraine.

(71) “Mathematical Analysis, Differential Equations and Their Applications Eastern Medi-

terranean University, Famagusta-North Cyprus, September 12-15, 2008.

(72) “Functional Methods in Approximation Theory and operator theory III August 22-26,

2009, Village Svityaz, Volyn, Ukraine.

(73) UKRAINIAN MATHEMATICAL CONGRESS – 2009 (Dedicated to the Centennial of

Nikolai N. Bogoliubov) Kyiv, Institute of Mathematics of NASU, August 27-29, 2009.

(74) 6th Maratea Conference FAAT 2009, Acquafredda di Maratea, September 24 – 30, 2009.

(75) I Jaen Conference on Approximation Theory, Ubeda, Jaen, Spain, July 4-9, 2010.

(76) International conference “Approximation theory”(Moscow, Russia, 23-26 August, 2010),

dedicated to the 90-th anniversary of Sergei Borisovich Stechkin (6.09.1920–22,11.1995).

(77) International conference “Modern problems of analysis”dedicated to the 70-th anni-

versary of the department of mathematical analysis of the Chernivtsi university, 30.09.2010-

3.10.2010.

(78) International conference on Modern Analysis, Donetsk, June 20-23, 2011.

(79) II Jaen Conference on Approximation Theory, Ubeda, Jaen, Spain, 26 June- 1 July,

2011.

(80) Complex Analysis and its Applications, International Conference dedicated to the 70th

anniversary of A.F. Grishin, Kharkiv, August 15-18, 2011.

(81) conference

(82) Research Workshop of the Israel Science Foundation “New Trends in Approximation

Theory Ein-Gedi, Israel, January 4-7, 2012.

(83) International conference “Theory of functions and problems of harmonic analysis” dedi-

cated to acad. Ibrahim Ibrahimov‘s 100th jubilee, February 28, 2012.

(84) MADEA 2012 International Conference on Mathematical Analysis, Differential Equati-

ons and their Applications, Mersin, Turkey, September 4-9, 2012.

(85) Bogoluybov readings DIF 2013. Differential equations, theory of functions and their

applications on the occasion of the 75th anniversary of academician A. M. Samoilenko,

June 23-30, 2013 Sevastopol, Ukraine.

(86) International Workshop on Approximation Theorey and Applications, dedicated to Gi-

useppe Mastroianni on the occasion of his retirement, Rifrteddo, Italy, September 12-13,

2013.

(87) International conference “Nonlinear Approximations and Applications”dedicated to the

60th birthday of Professor V. N. Temlyakov (October 29–November 01, 2013, Steklov

Mathematical Institute of RAS, Moscow).

(88) Conference “Stochastics and the infinite-dimensional analysis”, dedicated to 60-th anni-

versary of Kondratiev Yurii Hryhorovych, November 15, 2013, Kyiv.

(89) Conference “Methods of teaching mathematics in secondary and higher education”,

dedicated to the 75th anniversary of Kolesnyk Tamara Vsevolodivna, December 4-5,

2013, Kyiv.

(90) Kolloquium zur Approximationstheorie anl*a*sslich des 65. Geburtstages von Prof.Dr.dr.h.c.

Heiner Gonska, Fritag 27, Juni 2014, Duisburg.

(91) 2014 CMS Summer Meeting, The Delta Winnipeg – June 6-9.

(92) Conference on Approximation Theory, July 2014, Lijang, China.

(93) International meeting in honor of Professor Amnon Jakimovski’s 90th birthday, 10.6.15

– 11.6.15, TelAviv University.

(94) MADEA-7, Azerbaijan-Turkey-Ukrainian International Scientific Conference “Mathemati-

cal Analysis, Differential Equations and their Applications”, MADEA-7, September 08-

13, 2015, Baku – Azderbaijan.

(95) Approximation Theory and its Applications, International Conference dedicated to

75th anniversary of Professor Vitalii Pavlovych Motornyi, October 8-11, 2015, Dni-

propetrovsk, Ukraine.

(96) International Conference in Approximation Theory, May 8-11, 2017, Georgia Southern

University, USA.

(97) Workshop on mathematical analysis and applications in Tel Aviv on Oct.16th-19th.

Israel, 2017.

(98) 8th International Conference on “Mathematical Analysis, Differential Equation & Appli-

cations – MADEA 8 dedicated to the 80th birthday of Academician A. M. Samoilenko

(June 17–23, 2018, Kyrgyz-Turkish Manas University, Cholpon-Ata (Issyk-Kul), Kyrgyz

Republik)

(99) 9th International Conference on Curves and Surfaces, organised by SMAI-SIGMA. From

June 28 to July 4, 2018 at the Palais des Congres in Arcachon, France.

(100) International Conference ≪Functional Methods in Approximation Theory, Differential

Equations and Numerical Mathematics IV≫, Dedicated to the 100th anniversary of V.

- DZYADYK (1919-1998) Svityaz’ village, Volyn’ region, Ukraine June 20 – 26, 2019

Visiting professor

(1) Beijing normal university – 2014

(2) Belorussian State University – 1993

(3) Brno University – 1997

(4) CNRS,Lumini,CPT,Marseille,France – 1993, 2001

(5) Duisburg University – 1998

(6) Karlstad University – 2007

(7) Mersin University – 2002-2003

(8) Norwegian University of Science and Technology Trondheim – 2016

(9) Saratov State University – 1993

(10) Technische Hochschule Darmstadt – 1997

(11) Tel-Aviv University – 1994 – 2020

(12) Toulon and Var University – 1995,1999, 2012, 2014.

(13) University of Alberta – 2002

(14) University of Manitoba – 2002, 2011,2014

(15) University of South Carolina – 1996, 2000

Awards

(1) Republic Ostrovsky prize for young scientists – 1980

(2) Krylov prize of National Acad. of Sci. of Ukraine – 1991

(3) Soros grant for scientists and professors – 1998

(4) “Best professor of the year” at Kyiv University – 2000

(5) Medal “Vidminnyk osvity” – 2003

(6) Ukrainian Cabinet of Ministry honorable diploma – 2006

(7) Suprim Soviet of Ukraine, honorable diploma, 2009

(8) Ostrogradskii prize of National Acad. of Sci. of Ukraine – 2015

(9) Dragomanov gold medal – 2017

(10) Honored Education Worker of Ukraine – 2018

Candidate (of Phi. & Math. Sci. ) thesis

(1) Galan V.D., IM, 08.10.1991

(2) Shah L.G., IM, 15.06.1993

(3) Listopad V.V., IM, 08.06.1994

(4) Dzyubenko G.A., IM, 14.03.1995

(5) Djuzhenkova O.Yu., IM, 26.12.1995

(6) Pleshakov M.G., Saratov State University, 03.1998

(7) Usenko E.G., IM, 05.02.2002

(8) Popov P.A., IM, 18.05.2004

(9) Zhelnov O.D., IM, 18.05.2004

(10) Prymak A.V., IM, 17.01.2006

(11) Nesterenko O.N., IM, 30.01.2007

(12) Manzhos T.V., IM, 30.01.2007

(13) Viazovska M.S., IM, 11.05.2010, her awards:

Salem Prize 2016,

SASTRA Ramanujan Prize 2017,

Clay Research Award 2017,

European Prize in Combinatorics 2017,

New Horizons in Mathematics Prize, 2018

Ruth Lyttle Satter Prize in Mathematics, 2019

Fermat Prize, 2019

EMS Prize, 2020

The National Latsis Prize 2020

(14) Zherebko T.M., IM, 15.05.2012

(15) Radchenko D.V., IM, 14.03.2017, his award:

Ninth Popov Prize, 2020

(16) Bezkryla S. I., IM, 16.10.2018

PhD thesis

(1) Kopotun K.A., University of Alberta, 10.04.1996

(2) Yushchenko Lyudmila.Yu., University of Toulon and Var, 13.03.2002

(3) Bondarenko A.V., University of Toulon and Var, 25.01.2006, his awards:

Prize of Shevchenko Scientific Society (USA) and U.S.-Ukraine Foundation, 2011,

Seventh Popov Prize, Texas, 2013

The Royal Norwegian Society of Sciences and Letters annual prize for young researchers,

2014.

(4) Yushchenko Lidija.Yu., University of Toulon and Var, 1?.02.2010

Doctor (of Phi. & Math. Sci. ) thesis

(1) Korenovskii A.O. IM, 6.03.2007

(2) Bondarenko A.V. IM, 2021?

Books

(1) Approximation by polynomials and traces of functions, continuous on the segment, Kyiv,

Naukova dumka, 1992, 225 pages. (in Russian)

(2) Approximation Theory and its applications. Proceedings of the international conference,

dedicated to the memory of V.K.Dzjadyk. Editors: O.I. Stepanets and I.O.Shevchuk.

Kyiv, IM, 2000, 495 pages.

(3) Theory of Uniform Approximation of Functions by Polynomials, Walter de Gruyter,

2008, 496 pages (with Dzyadyk V.K.).

Papers

(4) On limiting values of an integral of Cauchy type for functions of Zygmund classes,

Ukrain. math. J. 24(1972), translation from Ukr. Mat. Zh (1973) №5, (with Dzjadyk

V.K.), 483-496,. 258.30034

(5) On a constructive characterization of functions from the classes *DrH!*2(*t*) on closed sets

with a piecewise smooth boundary, Ukrain. math. J. 25, 66-73 (1973).261.30028 MATH

(6) Some remarks about functions of type of modulus of continuity of order *k _ *2, in:

“Questions of the theory of approximation of functions and its applications Collect. sci.

Works, IM, Kyiv, 194-200 (1976) (in Russian).

(7) Solid and countour properties of analytic functions, in the termins of the second modulus

of continuity, in: “Questions of the theory of approximation of functions and its appli-

cations Collect. sci. Works, IM, Kyiv, 200-204 (1976) (in Russian).

(8) The classes of function *Hφ*(*t*)

*k;M *on sets *M *of the complex plane, in: “The theory of the

approximation of functions Proc. Int. Conf. Collect. Artic. Kaluga 1975, 409-412 (1977).

(9) Vladislav Kirillovich Dzyadyk, Russ. Math. Surv. 34 (1979), No. 4, 213-221 (with

Kornejchuk, N. P.; Nikol’skij, S. M.).

(10) Constructive characterization of classes of continuous functions of *M _ C *for the *k*-th

modulus of continuity, Math. Notes 25 (1979), 117-129 ; translation from Mat. Zametki

25 (1979),225-247 .

(11) Contour-solid theorems for Hoelder classes, in: “Questions of the theory of approximati-

on of functions Collect. sci. Works, IM, Kyiv, 186-189 (1980) (in Russian).

(12) Ueber die *k*-ten Stetigkeitsmoduln von Funktionen einer reellen und einer komplexen

Veraenderlichen, in: “Constructive function theory Proc. int. Conf., Blagoevgrad 1977,

191-194 (1980) (in Russiam).

(13) Smoothness properties and polynomial approximation, in: “Approximation and function

spaces Proc. int. Conf., Gdansk 1979, 686-694 (1981).

(14) Smoothness of an analytic function on a set and on its boundary, in: “Methods of

approximation theory and their applications Collect. sci. Works, IM, Kyiv, 123-133

(1982) (in Russian).

(15) Continuation of functions being, on an arbitrary set of a straight line, traces of functions

with given second modulus of continuity, Math. USSR, Izv. 22 (1984), No. 2, 227-246

; translation from Izv. Akad. Nauk SSSR, Ser. Mat. 47 (1983), No. 2, 248-267 (with

Dzjadyk V.K.).

(16) On traces of functions of class *Hφ*

*k *on the line, Sov. Math., Dokl. 28 (1983), 652-653 ;

translation from Dokl. Akad. Nauk SSSR 273 (1983), 313-314 .

(17) Extension of functions, which are traces of functions belonging to *Hφ*

*k *on an arbitrary

subset of the line. Anal. Math. 10 (1984), no. 3, 249–273.

(18) Properties of Dzjadyk’s polynomial kernels, Ukr. Math. J. 37 (1985), 114-116 ; translati-

on from Ukr. Mat. Zh. 37 (1985), No. 1, 130-132 .

(19) Uniform approximation of functions on an interval, Math. Notes 40 (1986), 521-528 ;

translation from Mat. Zametki 40 (1986), No. 1, 36-48 .

(20) Addendum to direct approximation theorems of S.M. Nikol’skij type on an interval, and

inverse theorems, Theory of functions and related questions of analysis, Proceedings

of a conference on function theory honoring the 80th birthday of Academician Sergej

Mikhajlovich Nikol’skij. Collection of papers, Trudy Mat. Inst. Steklov., 180, Nauka,

Moscow, 1987, 230–232; Proc. Steklov Inst. Math., 180 (1989), 273–274. 709.41542

MATH

(21) Properties of the Dzyadyk polynomial kernels on a closed segment, Ukr. Math. J. bf 41

(1989), No. 4, 457-461 ; translation from Ukr. Mat. Zh. 41 (1989), No. 4, 524-530 .

(22) On coapproximation of monotone functions, Sov. Math., Dokl. 40 (1990), No. 2, 349-354

; translation from Dokl. Akad. Nauk SSSR 308 (1989), No. 3, 537-541 .

(23) Dzyadyk’s research on the theory of approximation of functions of a complex variable,

Ukr. Math. J. 41 (1989), No. 4, 384-395 ; translation from Ukr. Mat. Zh. 41 (1989),

No. 4, 441-454 (with Belyj, V. I.; Golub, A. P.).

(24) On the sharpness of an approximation criterion of smoothness for functions on a segment,

Approximation and function spaces, Proc. 27th Semest., Warsaw / Pol. 1986, Banach

Cent. Publ. 22 (1989), 401-411 .

(25) A. Vladislav Kirillovich Dzyadyk (on the occasion of his seventieth birthday), Uspekhi

Mat. Nauk 44 (1989), no. 4(268), 243–244; translation in Russian Math. Surveys 44

(1989), no. 4, 213–215 (with Nikolskii S.M., Korneichuk N.P)

(26) Approximation of monotone functions by monotone polynomials, Russ. Acad. Sci., Sb.,

Math. 76 (1993), No. 1, 51-64 ; translation from Mat. Sb. 183 (1992), No. 5, 63-78 .

(27) On one negative result connected with Marchaud inequality, in: “Fourier series: theory

and applications”Collect. sci. Works, IM, Kyiv, 160-166 (1992) (in Russian, with Shah

L.G).

(28) Uniform estimates for monotonic polynomial approximation, Ukr. Math. J. 45 (1993),

No. 1, 40-47 ; translation from Ukr. Mat. Zh. 45 (1993), No. 1, 38-43 (with Dzyubenko,

- A.; Listopad).

(29) Whitney’s inequality and coapproximation, Proceedings of the XIXWorkshop on Functi-

on Theory (Beloretsk, 1994). East J. Approx. 1 (1995), no. 4, 479–500.

(30) Counter examples in convex and higher order constrained approximation, East J. Approx.

1 (1995), No. 3, 391-398 (with Leviatan D.).

(31) Comonotone approximation, Fundamentalnaya i prikladnaya matematika, 2(1996), 319-

363 (in Russian, with Gilewicz J.)

(32) One example in monotone approximation, J. Approximation Theory 86 (1996), No. 3,

270-277.

(33) Some positive results and counterexamples in comonotone approximation, J. Approxi-

mation Theory 89 (1997), No. 2, 195-206(with Leviatan D.).

(34) Remark on Lebesgue constant of Rogozinsky kernel, Ukrain. math. J. 49 (1997), N7,

1002-1004 (in Ukrainian, with Dzjadyk V.K.), translation in Ukrain. math. J. 49 (1997),

N7, 1125-1128 (1998).

(35) Approximation of monotone functions- a counter example, in: “Proceedings Chamonix

1996 A. Le M´ehaut´e, C. Rabut and L. L. Schumaker (eds.), Vanderbilt University Press,

Nashville TN (1997), 95-102 (with DeVore R.A., Leviatan D.).

(36) One construction of cubic convex spline, Approximation and optimization, Vol. I(Cluj-

Napoca, 1996), 357-368, Transilvania, Cluj-Napoca, 1997.

(37) DT – moduli of smoothness on domains with corners (in Ukrainian). Theory of approxi-

mation of functions(Russian) (Donetsk, 1998), 65-70, Tr. Inst. Prikl. Mat. Mekh., Donetsk,

1998.(with O.Yu. Djuzhenkova)

(38) Monotone approximation involving the third modulus of smoothness. Approximati-

on Theory IX, Vol. I. (Nashville, TN, 1998), 223-230, Innov.Appl.Math., Vanderbilt

Univ.Press, Nashville, TN, 1998.(with D.Leviatan)

(39) Nearly comonotone approximation, J. Approx. Theory, 95(1998), 53-81 (with D.Leviatan).

(40) Piecewise monotone pointwise approximation, Constructive approximation, 14 (1998),

311-348 (with G.A. Dzyubenko, J. Gilewicz ).

(41) Constants in comonotone polynomial approximation – a survey. New developments in

approximation theory (Dortmund, 1998), 145-158, Internat. Ser. Numer.Math., 132,

Birkhauser, Basel, 1999 (with D.Leviatan).

(42) The degree of coconvex polynomial approximation, Proc. Amer. Math. Soc., 127 (1999),

no.2, 409-415 (with K. Kopotun, ; D. Leviatan).

(43) Some positive results and counterexamples in comonotone approximation II, J. Approxi-

mation Theory, 100 (1999), 113-143 (with D. Leviatan ).

(44) Olympiad of mechanical and mathematical faculty. In the World of Math., 5 (1999),

N1, 72-73 (Ukrainian, with A.G.Kukush, V.V.Nekrashevich, A.M.Stanzhitskii).

(45) A brief survey of the scientific work of E. A. Storozhenko. (Russian) Ukrain. Math. Zh.

52 (2000), no. 4, 463-473 translation in Ukrainian math. Zh. 52 (2000), no. 4, 531-542

(with B.S.Kashin, N.P. Korneichuk, P.L. Ulyanov and V.A. Andrienko).

(46) Nearly comonotone approximation. II. Acta Sci. math. (Szeged) 66 (2000), no. 1-2,

115-135 (with D.Leviatan).

(47) More on comonotone polynomial approximation. Constr Approx. 16 (2000), no.4, 475-

486 (with D.Leviatan).

(48) Interpolatory pointwise estimates for polynomial approximation. Constr Approx. 16

(2000), no.4, 603-629 (with H.H.Gonska, D.Leviatan and H.-J. Wenz).

(49) Coconvex approximation. J. Approx. theory. 118 (2002), 20-65 (with D.Leviatan).

(50) Boudedness by 3 of Whitney interpolation constant. J. Approx. theory. 119 (2002),

271-290 (with J. Gilewicz and Yu. V. Kryakin).

(51) Oleksandr Ivanovych Stepanets’ (On His 60th Birthday). Ukrain. math. J. 54 (2002),

579-580 (with Yu. A. Mitropol’skii, A. M. Samoilenko, I. O. Lukovs’kyi and others).

English translation: Ukrain. math. J. 54 (2002), 711-712.

(52) Coconvex pointwise approximation. Ukrain. math. J. 54 (2002), 1200-1212 ( with G. A.

Dzyubenko and J. Gilewicz). English translation: Ukrain. math. J. 54 (2002), 1445-1461.

(53) Nearly coconvex approximation. Serdica Math. J. 28 (2002), 361-378. (with D.Leviatan).

(54) Coconvex polynomial approximation. J. Approx. theory 121 (2003), 100-118 (with

D.Leviatan).

(55) Linear bounded operator for extension of traces of differentiable functions on R. East

Journal on Approximations 10 (2004) 1-26 (with O.D.Zhelnov)

(56) Shape preserving approximation by splines, Naukovi zapysky KNU imeni Tarasa 8

(2004) 74-80 (with A.V.Prymak, in Ukrainian)

(57) Uniform estimates for polynomial approximation in domains with corners. J. Approx.

Theory 137 (2005), no. 2, 143-165 (with F. G. Abdullaev).

(58) Convex polynomial approximation in the uniform norm: conclusion. *Canad. J.Math*. 57

(2005), no. 6, 1224-1248 (with K.A.Kopotun and D. Leviatan).

(59) Coconvex approximation in the uniform norm: the final frontier. *Acta Math. Hungar*.

110 (2006), no. 1-2, 117-151 (with K. Kopotun and D. Leviatan ).

(60) Erratum to: “Coconvex approximation in the uniform norm: the final frontier”. *Acta*

*Math. Hungar*. 113 (2006), no. 3, 255 (with K. Kopotun and D. Leviatan).

(61) New phenomena in coconvex approximation. Anal. Math. 32 (2006), no. 2, 113-121

(with G.A. Dzyubenko and J. Gilewicz).

(62) Are the degrees of best (co)convex and unconstrained polynomial approximation the

same? *Acta Math.Hungar*. 123 (3) (2009), 273-290 (with K.A.Kopotun and D.Leviatan).

IF0.522

(63) Are the degrees of best (co)convex and unconstrained polynomial approximation the

same? II *Ukrainian Mathematical Journal*, 62 (2010), N3, October, 420-440 (Ukrainian

Original 62 (2010), N3, March, 369–386), (with K.A.Kopotun and D.Leviatan) IF0.167

https://doi.org/10.1007/s11253-010-0362-2

(64) Nikolskii-type estimates for coconvex approximation of functions with one inflection

point. *Jaen J. on Approximations*. 2(1) (2010), 51-64 (with G. A. Dzyubenko and D.

Leviatan).

(65) Coconvex pointwise approximation. *Rendiconti del Circolo Matematico di Palermo Serie*

*II*, 82 (2010), pp. 359-374. (with G. A. Dzyubenko and D. Leviatan).

(66) One property of domains with corners. *Collect. sci. Works, Inst. of Math. NAN of*

*Ukraine *8 (2011), 5 pg. (with F.G.Abdullaev and T.M.Zherebko).

(67) Uniform and pointwise shape preserving approximation by algebraic polynomials. *Surveys*

*in Approx. Theory *6 (2011), 24-74. (with K. A. Kopotun, D. Leviatan and A. Prymak).

(68) Shape-preserving projections settings and the comonotone case. *Ukrainian Mathematical*

*Journal*, 64 (2012), N5, October, 767-780 (Ukrainian Original 64, N5, May, 2012, 674-

684), (with M.Prophet). IF0.154

(69) Positive results and counterexamples in comonotone approximation. *Constructive Approxi-*

*mation*, 36 (2012), 243-266. (with D.Radchenko and D.Leviatan). IF1.068

(70) 65 years since the paper “On the value of the best approximation of functions with a

real singular point”by I. I. Ibragimov. *Azerbaijan J. Math.*, 2 (2012), N2, 94-104. (with

D.Leviatan).

(71) Locally univalent approximation by polynomials, “Complex Analysis, Potential theory

and Applications”(dedicated to Professor Promarz Melikovich Tamrazov), *Transactions*

*of the Institute of Mathematics of the National Academy of Sciences of Ukraine*, 10

(2013) N 4–5, 570-574 (in Ukrainian). (with Yu. S. Semikina and T. M. Zherebko)

(72) Pointwise estimates of coconvex approximation, *Jaen J. Approx. *6(2) (2014), 261-295.

( with G.A.Dzyubenko and D. Leviatan).

(73) Positive results and counterexamples in comonotone approximation II, *J. Approx. Theory*,

179 (2014), 1-23 (with D.Leviatan, and O.V.Vlasiuk). IF0.951

(74) New moduli of smoothness, *Publications de l’institut math*_*e**matique Nouvelle s*_*e**rie*, 96

(110) (2014), 169–180. DOI: (with K.A. Kopotun, and D. Leviatan) 10.2298/PIM1410169K

IF0.152

(75) New Moduli of Smoothness:Weighted DT Moduli Revisited and Applied, *Constr. Approx.*,

41 (2015), 129-159 (with K. A. Kopotun *_*and D. Leviatan). DOI 10.1007/s00365-014-

9270-2. IF1.346

(76) Motornyi Vitalii Pavlovych (to 75-th anniversary), Ukr. Math. J, 67 (2015), №7, 995-

999 ( with A. M. Samoilenko and 12 co-authors, in Ukrainian).

(77) Constrained approximation with Jacobi weights, *Canadian Journal of Mathematics*,

68(2016), N1, 109-128 ( with K. A. Kopotun and D. Leviatan). DOI: https://doi.org/10.4153/CJM-

2015-034-4 IF0.963

(78) Interpolation and Lagrange Hermite devided differences, *U sviti matematyky*, 22 (2016)

N2 ( with M. V. Shcheglov, in Ukrainian)

(79) Jackson type estimates for piecewise q-monotone approximation, *q _ *3, are not valid,

*Pure and Applied Functional Analysis*, 1, (2016), N1, 85-96 (with D.Leviatan).

(80) Yet another look at positive linear operators, *q*-monotonicity and applications *Journal*

*of Approximation Theory*, 210 (2016), 1-22 (with K. A. Kopotun , A. Prymak and D.

Leviatan. https://doi.org/10.1016/j.jat.2016.06.001 IF0.931

(81) Comparing the degrees of unconstrained and shape preserving approximation by polynomi-

als, *Journal of Approximation Theory*, 211 (2016), 16-28(with D.Leviatan). https://doi.org/10.1016/j.jat.2016.07.004

IF0.931

(82) Exact constant in Dzyadyk’s inequality for the derivative of an algebraic polynomi-

al, *Ukr. Math. J. *69 (2017), № 5, 624-630 (with V.D.Halan, in Ukrainian). Ehglish

translation: *Ukrainian Mathematical Journal*, 69 (2017), № 5, 725-733. IF*_*0.228

(83) On moduli of smoothness with Jacobi weights, *Ukr. Math. J. *70 (2018), № 2, 379-403

(with K. A. Kopotun and D. Leviatan). Ehglish translation: *Ukrainian Mathematical*

*Journal*, 70 (2018), № 3, 437-466. IF*_*0.228

(84) Interpolatory pointwise estimates for monotone polynomial approximation, *Journal*

*of Mathematical Analysis and Applications*, 459 (2018), № 2, 1260-1295 (with K. A.

Kopotun and D. Leviatan). https://doi.org/10.1016/j.jmaa.2017.11.038 IF*_*1.064

(85) Vladyslav Kyrylovych Dzyadyk (on His 100th Birthday), *Ukrainian Mathematical Journal*

71 (2019), No. 2, July, 2019, Pages 167-170 (Ukrainian Original Vol. 71, No. 2, February,

2019, 147 – 150) (with Samoilenko, A. M.; Zadiraka, V. K.; Letychevs’kyi, O. A.;. . . ).

IF*_*0.343 doi.org/10.1007/S11253-019-01635-6

(86) One estimate for divided differences and its applications, *Ukr. Math. J. *71 (2019),

№ 2, 230–245 (with K. A. Kopotun and D. Leviatan). Ehglish translation: *Ukrainian*

*Mathematical Journal*, 71 (2019), № 2, 259-277 (with K. A. Kopotun and D. Leviatan).

IF*_*0.343 DOI 10.1007/s11253-019-01643-6

(87) Interpolatory estimates for convex piecewise polynomial approximation, *Journal of Mathemati-*

*cal Analysis and Applications *474 (2019), № 1, 467-479 (with K. A. Kopotun and D.

Leviatan). https://doi.org/10.1016/j.jmaa.2019.01.055 IF*_*1.188

(88) On weighted approximation with Jacobi weights Pages 96-112 K. A. Kopotun, D. Levi-

atan, I. A. Shevchuk *Journal of Approximation Theory*, 237 (2019), 96-112 (with K. A.

Kopotun and D.Leviatan). https://doi.org/10.1016/j.jat.2018.09.003 IF*_*1.022

(89) On Some Properties of Moduli of Smoothness with Jacobi Weights, *in book: Topics in*

*Classical and Modern Analysis, M.Abell et al. (eds.), Topics in Applied and Numerical*

*Harmonic Analysis*, Springer Nature Switzerland AG 2019 October, 19-31 (with K. A.

Kopotun and D. Leviatan). DOI: 10.1007/978-3-030-12277-5-1

(90) Uniform and pointwise shape preserving approximation (SPA) by algebraic polynomials:

an update. *The SMAI journal of computational mathematics*, 5 (2019) , 99-108 (with

- A. Kopotun and D.Leviatan). doi : 10.5802/smai-jcm.54. https://smai-jcm.centre-

mersenne.org/item/SMAI-JCM

(91) Interpolatory pointwise estimates for convex polynomial approximation, *Acta Mathemati-*

*ca Hungarica*, 263, 33 pg., to appear (with K. A. Kopotun, D. Leviatan and I. L.

Petrova). DOI: 10.1007/s10474-020-01063-0

Preprints and referats

(92) On Plemelj-Privalov theorem and constructive characteristic of functions of Zygmund

class, Preprint IM-72-3 (1972) (in Russian)

(93) On Plemelj-Privalov theorem and constructive characteristic of functions of Zygmund

class, Autoreferat of candidate dissertation, Kyiv, IM (1973) (in Russian)

(94) Constructive description of traces of differentiable functions of a real variable, Preprint

IM-83-19, Kyiv (1983), 40 pp. (in Russian). 86d:46030, 46E35 (41A35)

(95) Extension and approximation of smooth functions of one variable, Autoreferat of doctor

dissertation, Kyiv, IM (1985) (in Russian)

(96) Comonotone approximation and polynomial Dzyadyk kernels, Preprint IM-89-10, Kyiv

(1989), 27 pp. (in Russian) 90m:41018, 41A10

(97) Comonotone approximation poinwise estimates for twice differentiable function , Prepri-

nt, September 1994, CPT-94/P.3067 CNRS Lumini, Marseille, France (with Dzyubenko

G.A., Listopad V.V)

(98) Piecewise monotone pointwise approximations, Preprint, 1994, CPT-94/P.3121 CNRS

Lumini, Marseille, France (with Dzyubenko G.A., Gilewicz J.)

(99) Comonotone approximation, Preprint, 1995, CPT-95/P.3203 CNRS Lumini, Marseille,

France, 41pg. (with Dzyubenko G.A., Gilewicz J.)

(100) One example in monotone approximation, in “Preprint series IM, Kyiv, Preprint 94.40

(1995), 8pg.

(101) Interpolatory pointwise estimates for polynomial approximation. Constr Approx. Prepri-

nt, Duisburg University, 1998 (with H.H.Gonska, D.Leviatan and H.-J. Wenz).

(102) Whitney interpolatory constants are bounded by 3. Preprint, CPT, CNRS, Lumini,

Marseille, France (2001) (with J. Gilewicz and Yu. V. Kryakin).

(103) Weighted D-T moduli revisited and applied, CRM Barcelona, Spain, Preprint num.

1136, January 2013, 1-20.(with K.Kopotun and D.Leviatan).

Industry applications

(1) Dai, M., Loguinov, D., Radha, H.M., Rate-distortion analysis and quality control in

scalable Internet streaming, IEEE Transactions on Multimedia, 8 (2006), N6, 1135-

1146.

(2) David L. Russel, Computing convex spline approximation, International Journal of

Information and Systems Sciences, 5 (2006), N1, 83–97.

(3) Tian, D.-G., Huang, Y.-Q., Computation of channel capacity based on self-concordant

functions, Journal of Electrical and Computer Engineering, 2012 (2012), Article ID

318946, 9 p.

(4) Kevin Murray, SamuelM¨uller, Berwin A. Turlach, Fast and flexible methods for monotone

polynomial fitting, Journal of Statistical Computation and Simulation 86(15) (February

2016):1-21 DOI10.1080/00949655.2016.1139582

(5) Ren-Hong Wang, Multivariate spline and algebraic geometry, Journal of Computati-

onal and Applied Mathematics 121(1-2)(September 2000):153-163 DOI10.1016/S0377-

0427(00)00344-7.

(6) Simon Foucart, Vladlena Powers, Constrained approximation by semidefinite programmi-

ng, IMA Journal of Numerical Analysis, 37 (April 2017), N2, 1066–1085,

https://doi.org/10.1093/imanum/drw014

(7) Vladimir Kodnyako, Directional splines for economic analytics, Economic Computation

and Economic Cybernetics Studies and Research, 54 (2020), N3, 129-144,

DOI: 10.24818/18423264/54.3.20.08

Main Scientific Directions

(1) Complex polynomial approximation. The theory of constructive approximation by

algebraic polynomials is developed on the sets *E _ ***C **with piecewise smooth boundary

for the functions, having a high order of smoothness.

(2) Extension from an arbitrary set *E _ ***R**. Necessary and sufficient condition on the

values of a function *f *defined on *E *is obtained for the function *f *would be the trace of

a function *F*, belonging to Sobolev, Helder, generalized Helder class.

(3) Shape Preserving Approximation. In all cases of their validity the estimates for

the error of polynomial monotone and comonotone approximation of functions defined

in a closed interval are proved, which have the same form as well-known unconstrained

Jackson type, pointwise, Ditzian – Totik estimates. In all other cases corresponding

countrexamples are constructed.

Other results

(1) (1980) Sewell’s problem about contour – solid properties of functions *f*, analytic in

*E _ ***C **and continuous on *E *is solved, in the case when *E *is an arbitrary closed set,

and *f 2 Lip_; _ > *0.

(2) (1989) Hasson’s conjecture about an approximation criteria of smoothness is proved.

(3) (1989) DeVore and Yu’s problem about the pointwise estimate of monotone approxi-

mation of functions belonging to Sobolev class *Wr; r > *2, is solved.

(4) (1997) The exact values of Lebesgue constants of Rogozinsky kernels are obtained.

(5) (2002) In the Sendov’s problem about the interpolational Whitney constant *w *the new

estimate *w < *3 is proved. The previous estimate was *w < *5, Sendov’s conjecture is

*w _ *2.

Social activity

(1) Chair (co-chair, vice-chair) of the organizing commitee of the inernational conferences

held in Kyiv (1991, 1999, 2001, 2004, 2009, 2015), Rivne (1996), Mersin (2004, 2012),

Uzghorod(2006), Famagusta(2008), Svityaz(2009,2019), Baku(2015), Issyk-Kul(2018),

Dnipro(2020). Science secretary of the inernational conference held in Kyiv in 1983.

(2) Member of the Science Soviet on the defense of doctor dissertations in the IM.

(3) Head of the jury of students competitions in Mech.Math.faculty.

(4) Head of methodology commission in the Ministry of education of Ukraine

(5) Member of editorial board of 6 journals.

(6) Member of expert commission of VAK of Ukraine.