Edit Profile Shevchuk, Igor A. Compute Distance To: Compute Author ID: shevchuk.igor-a Published as: Shebchuk, Igor A.; Shevchuk, I. A.; Shevchuk, Igor; Shevchuk, Igor A. External Links: MGP · Wikidata Documents Indexed: 75 Publications since 1972, including 1 Book all top 5 Co-Authors 20 single-authored 34 Leviatan, Dany 16 Kopotun, Kirill A. 6 Dzyubenko, German A. 5 Dzyadyk, Vladyslav Kyrylovych 5 Gilewicz, Jacek 2 Abdullayev, Fahreddin G. 2 Belyj, V. I. 2 Golub, Anatoly P. 2 Korneĭchuk, Nikolaĭ Pavlovich 2 Prymak, Andriy V. 1 Andrienko, Vitaly Afanasevich 1 DeVore, Ronald A. 1 Gonska, Heinz Herbert 1 Kashin, Boris Sergeevich 1 Kryakin, Yuri V. 1 Leviatan, L. 1 Levitan, D. 1 Listopad, V. V. 1 Nikol’skiĭ, Sergeĭ Mikhaĭlovich 1 Prophet, Michael P. 1 Radchenko, Danylo V. 1 Ul’yanov, Pëtr Lavrent’evich 1 Vlasiuk, Oleksandr V. 1 Wenz, Hans-Jörg 1 Zhelnov, O. D. 1 Zherebko, T. M. all top 5 Serials 12 Journal of Approximation Theory 9 Ukrainian Mathematical Journal 7 Ukraïns’kyĭ Matematychnyĭ Zhurnal 5 Constructive Approximation 3 East Journal on Approximations 2 Journal of Mathematical Analysis and Applications 2 Mathematical Notes 2 Canadian Journal of Mathematics 2 Soviet Mathematics. Doklady 2 Acta Mathematica Hungarica 2 Jaen Journal on Approximation 1 Analysis Mathematica 1 Russian Mathematical Surveys 1 Acta Scientiarum Mathematicarum 1 Mathematics of the USSR. Izvestiya 1 Proceedings of the American Mathematical Society 1 Publications de l’Institut Mathématique. Nouvelle Série 1 Russian Academy of Sciences. Sbornik. Mathematics 1 Serdica Mathematical Journal 1 Fundamental’naya i Prikladnaya Matematika 1 Surveys in Approximation Theory (SAT) 1 Proceedings of the Steklov Institute of Mathematics 1 Zbirnyk Prats’ Instytutu Matematyky NAN Ukraïny 1 Azerbaijan Journal of Mathematics 1 Pure and Applied Functional Analysis 1 SMAI Journal of Computational Mathematics all top 5 Fields 59 Approximations and expansions (41-XX) 15 Functions of a complex variable (30-XX) 6 Functional analysis (46-XX) 4 Real functions (26-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 History and biography (01-XX) 1 Operator theory (47-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 49 Publications have been cited 261 times in 99 Documents Cited by ▼ Year ▼ Theory of uniform approximation of functions by polynomials. Transl. from the Russian by Dimitry Malyshev, Peter V. Malyshev and Vladimir V. Gorunovich. Zbl 1148.41003Dzyadyk, Vladislav K.; Shevchuk, Igor A. 34 2008 Approximation of monotone functions by monotone polynomials. Zbl 0782.41013Shevchuk, I. A. 28 1992 Uniform and pointwise shape preserving approximation by algebraic polynomials. Zbl 1296.41001Kopotun, K. A.; Leviatan, D.; Prymak, A.; Shevchuk, I. A. 15 2011 Piecewise monotone pointwise approximation. Zbl 0912.41007Dzyubenko, G. A.; Gilewicz, J.; Shevchuk, I. A. 14 1998 Interpolatory pointwise estimates for polynomial approximation. Zbl 0976.41018Gonska, H. H.; Leviatan, D.; Shevchuk, I. A.; Wenz, H.-J. 11 2000 Nearly comonotone approximation. Zbl 0911.41003Leviatan, D.; Shevchuk, I. A. 11 1998 Comonotone approximation. Zbl 0908.41003Gilewicz, J.; Shevchuk, I. A. 11 1996 New moduli of smoothness: weighted DT moduli revisited and applied. Zbl 1329.41020Kopotun, K. A.; Leviatan, D.; Shevchuk, I. A. 9 2015 The degree of coconvex polynomial approximation. Zbl 0914.41005Kopotun, K.; Leviatan, D.; Shevchuk, I. A. 9 1999 Convex polynomial approximation in the uniform norm: conclusion. Zbl 1102.41021Kopotun, K. A.; Levitan, D.; Shevchuk, I. A. 7 2005 Some positive results and counterexamples in comonotone approximation. II. Zbl 0934.41013Leviatan, D.; Shevchuk, I. A. 7 1999 New moduli of smoothness. Zbl 06694546Kopotun, K. A.; Leviatan, D.; Shevchuk, I. A. 6 2014 Are the degrees of the best (co)convex and unconstrained polynomial approximations the same? II. Zbl 1224.41019Kopotun, K.; Leviatan, D.; Shevchuk, I. A. 6 2010 Approximation of monotone functions: A counter example. Zbl 0958.41012DeVore, R. A.; Leviatan, D.; Shevchuk, I. A. 6 1997 Coconvex polynomial approximation. Zbl 1021.41006Leviatan, D.; Shevchuk, I. A. 5 2003 Coconvex approximation. Zbl 1057.41012Leviatan, D.; Shevchuk, I. A. 5 2002 Constructive characterization of classes of continuous functions of a set \(\mathfrak M\subset\mathbb{C}\) for the \(k-th\) modulus of continuity. Zbl 0431.30025Shevchuk, I. A. 5 1979 On limiting values of an integral of Cauchy type for functions of Zygmund classes. Zbl 0258.30034Dzyadyk, V. K.; Shevchuk, I. A. 5 1973 Positive results and counterexamples in comonotone approximation. Zbl 1254.41006Leviatan, D.; Radchenko, D. V.; Shevchuk, I. A. 4 2012 Some positive results and counterexamples in comonotone approximation. Zbl 0870.41016Leviatan, D.; Shevchuk, I. A. 4 1997 Constrained approximation with Jacobi weights. Zbl 1347.41019Kopotun, Kirill; Leviatan, Dany; Shevchuk, Igor 3 2016 Pointwise estimates of coconvex approximation. Zbl 1379.41005Dzyubenko, G. A.; Leviatan, D.; Shevchuk, I. A. 3 2014 Positive results and counterexamples in comonotone approximation. II. Zbl 1292.41003Leviatan, D.; Shevchuk, I. A.; Vlasiuk, O. V. 3 2014 Are the degrees of best (co)convex and unconstrained polynomial approximation the same? Zbl 1265.41010Kopotun, K.; Leviatan, D.; Shevchuk, I. A. 3 2009 Boundedness by 3 of the Whitney interpolation constant. Zbl 1099.41500Gilewicz, J.; Kryakin, Yu. V.; Shevchuk, I. A. 3 2002 Nearly comonotone approximation. II. Zbl 0963.41008Leviatan, D.; Shevchuk, I. A. 3 2000 More on comonotone polynomial approximation. Zbl 0959.41006Leviatan, D.; Shevchuk, I. A. 3 2000 Monotone approximation estimates involving the third modulus of smoothnes. Zbl 0939.41015Leviatan, Dany; Shebchuk, Igor A. 3 1998 One construction of cubic convex spline. Zbl 0888.41013Shevchuk, I. A. 3 1997 Counter examples in convex and higher order constrained approximation. Zbl 0846.41006Leviatan, D.; Shevchuk, I. A. 3 1995 Interpolatory estimates for convex piecewise polynomial approximation. Zbl 1414.41004Kopotun, K. A.; Leviatan, D.; Shevchuk, I. A. 2 2019 Interpolatory pointwise estimates for monotone polynomial approximation. Zbl 1377.41001Kopotun, K. A.; Leviatan, D.; Shevchuk, I. A. 2 2018 Comparing the degrees of unconstrained and shape preserving approximation by polynomials. Zbl 1353.41003Leviatan, D.; Shevchuk, I. A. 2 2016 New phenomena in coconvex approximation. Zbl 1108.41013Dzyubenko, G. A.; Gilewicz, J.; Shevchuk, I. A. 2 2006 Coconvex approximation in the uniform norm: the final frontier. Zbl 1102.41005Kopotun, K.; Leviatan, D.; Shevchuk, I. A. 2 2006 Constants in comonotone polynomial approximation. – A survey. Zbl 0938.41002Leviatan, L.; Shevchuk, I. A. 2 1999 One example in monotone approximation. Zbl 0868.41015Shevchuk, I. A. 2 1996 Uniform estimates for monotonic polynomial approximation. Zbl 0822.41015Dzyubenko, G. A.; Listopad, V. V.; Shevchuk, I. A. 2 1993 Properties of the Dzyadyk polynomial kernels on a closed segment. Zbl 0731.41008Shevchuk, I. A. 2 1989 On a constructive characterization of functions from the classes D\(^r H^{\omega_2(t)}\) on closed sets with a piecewise smooth boundary. Zbl 0261.30028Shevchuk, I. A. 2 1973 Jackson type estimates for piecewise \(q\)-monotone approximation, \(q\geq 3\), are not valid. Zbl 1347.41007Leviatan, Dany; Shevchuk, Igor A. 1 2016 Nikolskii-type estimates for coconvex approximation of functions with one inflection point. Zbl 1248.41014Dzyubenko, G. A.; Leviatan, D.; Shevchuk, I. A. 1 2010 Uniform estimates for polynomial approximation in domains with corners. Zbl 1089.30033Abdullayev, F. G.; Shevchuk, I. A. 1 2005 Linear bounded operator for extension of traces of differentiable functions on \(\mathbb R\). Zbl 1113.41004Shevchuk, I. A.; Zhelnov, O. D. 1 2004 Nearly coconvex approximation. Zbl 1044.41003Leviatan, D.; Shevchuk, I. A. 1 2002 Coconvex pointwise approximation. Zbl 1019.41003Dzyubenko, G. A.; Gilewicz, J.; Shevchuk, I. A. 1 2002 Whitney’s inequality and coapproximation. Zbl 0852.41015Shevchuk, I. A. 1 1995 On coapproximation of monotone functions. Zbl 0719.41011Shevchuk, I. A. 1 1990 Über Grenzwerte eines Integrals Cauchyschen Typs für Funktionen Zygmundscher Klassen. Zbl 0253.30025Dzyadyk, V. K.; Shevchuk, I. A. 1 1972 Interpolatory estimates for convex piecewise polynomial approximation. Zbl 1414.41004Kopotun, K. A.; Leviatan, D.; Shevchuk, I. A. 2 2019 Interpolatory pointwise estimates for monotone polynomial approximation. Zbl 1377.41001Kopotun, K. A.; Leviatan, D.; Shevchuk, I. A. 2 2018 Constrained approximation with Jacobi weights. Zbl 1347.41019Kopotun, Kirill; Leviatan, Dany; Shevchuk, Igor 3 2016 Comparing the degrees of unconstrained and shape preserving approximation by polynomials. Zbl 1353.41003Leviatan, D.; Shevchuk, I. A. 2 2016 Jackson type estimates for piecewise \(q\)-monotone approximation, \(q\geq 3\), are not valid. Zbl 1347.41007Leviatan, Dany; Shevchuk, Igor A. 1 2016 New moduli of smoothness: weighted DT moduli revisited and applied. Zbl 1329.41020Kopotun, K. A.; Leviatan, D.; Shevchuk, I. A. 9 2015 New moduli of smoothness. Zbl 06694546Kopotun, K. A.; Leviatan, D.; Shevchuk, I. A. 6 2014 Pointwise estimates of coconvex approximation. Zbl 1379.41005Dzyubenko, G. A.; Leviatan, D.; Shevchuk, I. A. 3 2014 Positive results and counterexamples in comonotone approximation. II. Zbl 1292.41003Leviatan, D.; Shevchuk, I. A.; Vlasiuk, O. V. 3 2014 Positive results and counterexamples in comonotone approximation. Zbl 1254.41006Leviatan, D.; Radchenko, D. V.; Shevchuk, I. A. 4 2012 Uniform and pointwise shape preserving approximation by algebraic polynomials. Zbl 1296.41001Kopotun, K. A.; Leviatan, D.; Prymak, A.; Shevchuk, I. A. 15 2011 Are the degrees of the best (co)convex and unconstrained polynomial approximations the same? II. Zbl 1224.41019Kopotun, K.; Leviatan, D.; Shevchuk, I. A. 6 2010 Nikolskii-type estimates for coconvex approximation of functions with one inflection point. Zbl 1248.41014Dzyubenko, G. A.; Leviatan, D.; Shevchuk, I. A. 1 2010 Are the degrees of best (co)convex and unconstrained polynomial approximation the same? Zbl 1265.41010Kopotun, K.; Leviatan, D.; Shevchuk, I. A. 3 2009 Theory of uniform approximation of functions by polynomials. Transl. from the Russian by Dimitry Malyshev, Peter V. Malyshev and Vladimir V. Gorunovich. Zbl 1148.41003Dzyadyk, Vladislav K.; Shevchuk, Igor A. 34 2008 New phenomena in coconvex approximation. Zbl 1108.41013Dzyubenko, G. A.; Gilewicz, J.; Shevchuk, I. A. 2 2006 Coconvex approximation in the uniform norm: the final frontier. Zbl 1102.41005Kopotun, K.; Leviatan, D.; Shevchuk, I. A. 2 2006 Convex polynomial approximation in the uniform norm: conclusion. Zbl 1102.41021Kopotun, K. A.; Levitan, D.; Shevchuk, I. A. 7 2005 Uniform estimates for polynomial approximation in domains with corners. Zbl 1089.30033Abdullayev, F. G.; Shevchuk, I. A. 1 2005 Linear bounded operator for extension of traces of differentiable functions on \(\mathbb R\). Zbl 1113.41004Shevchuk, I. A.; Zhelnov, O. D. 1 2004 Coconvex polynomial approximation. Zbl 1021.41006Leviatan, D.; Shevchuk, I. A. 5 2003 Coconvex approximation. Zbl 1057.41012Leviatan, D.; Shevchuk, I. A. 5 2002 Boundedness by 3 of the Whitney interpolation constant. Zbl 1099.41500Gilewicz, J.; Kryakin, Yu. V.; Shevchuk, I. A. 3 2002 Nearly coconvex approximation. Zbl 1044.41003Leviatan, D.; Shevchuk, I. A. 1 2002 Coconvex pointwise approximation. Zbl 1019.41003Dzyubenko, G. A.; Gilewicz, J.; Shevchuk, I. A. 1 2002 Interpolatory pointwise estimates for polynomial approximation. Zbl 0976.41018Gonska, H. H.; Leviatan, D.; Shevchuk, I. A.; Wenz, H.-J. 11 2000 Nearly comonotone approximation. II. Zbl 0963.41008Leviatan, D.; Shevchuk, I. A. 3 2000 More on comonotone polynomial approximation. Zbl 0959.41006Leviatan, D.; Shevchuk, I. A. 3 2000 The degree of coconvex polynomial approximation. Zbl 0914.41005Kopotun, K.; Leviatan, D.; Shevchuk, I. A. 9 1999 Some positive results and counterexamples in comonotone approximation. II. Zbl 0934.41013Leviatan, D.; Shevchuk, I. A. 7 1999 Constants in comonotone polynomial approximation. – A survey. Zbl 0938.41002Leviatan, L.; Shevchuk, I. A. 2 1999 Piecewise monotone pointwise approximation. Zbl 0912.41007Dzyubenko, G. A.; Gilewicz, J.; Shevchuk, I. A. 14 1998 Nearly comonotone approximation. Zbl 0911.41003Leviatan, D.; Shevchuk, I. A. 11 1998 Monotone approximation estimates involving the third modulus of smoothnes. Zbl 0939.41015Leviatan, Dany; Shebchuk, Igor A. 3 1998 Approximation of monotone functions: A counter example. Zbl 0958.41012DeVore, R. A.; Leviatan, D.; Shevchuk, I. A. 6 1997 Some positive results and counterexamples in comonotone approximation. Zbl 0870.41016Leviatan, D.; Shevchuk, I. A. 4 1997 One construction of cubic convex spline. Zbl 0888.41013Shevchuk, I. A. 3 1997 Comonotone approximation. Zbl 0908.41003Gilewicz, J.; Shevchuk, I. A. 11 1996 One example in monotone approximation. Zbl 0868.41015Shevchuk, I. A. 2 1996 Counter examples in convex and higher order constrained approximation. Zbl 0846.41006Leviatan, D.; Shevchuk, I. A. 3 1995 Whitney’s inequality and coapproximation. Zbl 0852.41015Shevchuk, I. A. 1 1995 Uniform estimates for monotonic polynomial approximation. Zbl 0822.41015Dzyubenko, G. A.; Listopad, V. V.; Shevchuk, I. A. 2 1993 Approximation of monotone functions by monotone polynomials. Zbl 0782.41013Shevchuk, I. A. 28 1992 On coapproximation of monotone functions. Zbl 0719.41011Shevchuk, I. A. 1 1990 Properties of the Dzyadyk polynomial kernels on a closed segment. Zbl 0731.41008Shevchuk, I. A. 2 1989 Constructive characterization of classes of continuous functions of a set \(\mathfrak M\subset\mathbb{C}\) for the \(k-th\) modulus of continuity. Zbl 0431.30025Shevchuk, I. A. 5 1979 On limiting values of an integral of Cauchy type for functions of Zygmund classes. Zbl 0258.30034Dzyadyk, V. K.; Shevchuk, I. A. 5 1973 On a constructive characterization of functions from the classes D\(^r H^{\omega_2(t)}\) on closed sets with a piecewise smooth boundary. Zbl 0261.30028Shevchuk, I. A. 2 1973 Über Grenzwerte eines Integrals Cauchyschen Typs für Funktionen Zygmundscher Klassen. Zbl 0253.30025Dzyadyk, V. K.; Shevchuk, I. A. 1 1972 all cited Publications top 5 cited Publications all top 5 Cited by 88 Authors 24 Leviatan, Dany 20 Shevchuk, Igor A. 18 Kopotun, Kirill A. 8 Dzyubenko, German A. 6 Andrievskii, Vladimir V. 6 Prymak, Andriy V. 4 Abdullayev, Fahreddin G. 4 Draganov, Borislav R. 4 Pleshakov, M. G. 3 Imashkyzy, Meerim 2 Forster, Brigitte 2 Ghorbanalizadeh, Arash M. 2 Hu, Yingkang 2 Petrova, I. L. 2 Sawano, Yoshihiro 2 Sun, Yiguo 2 Trigub, Roal’d Mikhaĭlovich 2 Vlasiuk, Oleksandr V. 1 Abdullayev, Gülnara A. 1 Akgun, Ramazan 1 Babenko, Aleksandr Grigor’evich 1 Balcı, Şölen 1 Belyj, V. I. 1 Beregova, Galyna 1 Bezkryla, S. I. 1 Blatt, Hans-Peter 1 Bondarenko, Andriy V. 1 Boytsov, Dmitry I. 1 Brudnyi, Yuri A. 1 Chaĭchenko, Stanislav Olegovich 1 Chaĭkovs’kyĭ, Andriĭ Volodymyrovych 1 Chyzhykov, Igor Elbertovych 1 Cuyt, Annie A. M. 1 Danelia, Akaki 1 Ditzian, Zeev 1 Dzyubenko, H. A. 1 Gadjev, Ivan 1 Gavrilyuk, I. G. 1 Gilewicz, Jacek 1 Golub, Anatoly P. 1 Guliyev, Vagif Sabir 1 Huang, Yi-Qun 1 Johanis, Michal 1 Kocić, Ljubiša M. 1 Kolomoitsev, Yurii S. 1 Kozlov, Inna 1 Kryakin, Yuri V. 1 Lindström, Torsten 1 Listopad, V. V. 1 Lomako, Tetiana 1 Lubinsky, Doron S. 1 Maizlish, Oleksandr 1 Makarov, V. E. 1 Malikov, Emir 1 Medvedev, Alexey N. 1 Milovanović, Gradimir V. 1 Müller, Samuel 1 Murray, Kevin 1 Nesterenko, Oleksiĭ Nykyforovych 1 Nguyen Hoa Thang 1 Pahirya, Mykhaylo M. 1 Pereverzev, Sergei V. 1 Prestin, Jurgen 1 Pritsker, Igor E. 1 Pupashenko, N. S. 1 Radchenko, Danylo V. 1 Ramazanov, Abdul-Rashid Kekhrimanovich 1 Révész, Szilárd György 1 Salazar Celis, Oliver 1 Semenova, Evgeniya V. 1 Shatalina, A. V. 1 Shidlich, Andriy L. 1 Shvartsman, Pavel 1 Sidorov, Sergeĭ Petrovich 1 Tian, Dagang 1 Tkachenko, Pavlo 1 Turlach, Berwin A. 1 Vakarchuk, Sergei Borisovich 1 Vakarchuk, Sergey B. 1 Varga, Richard Steven 1 Verma, Sudeep 1 Viazovska, Maryna S. 1 Vinogradov, Oleg Leonidovich 1 Viswanathan, Puthan Veedu 1 Yu, Xiangming 1 Zajíček, Luděk 1 Zherebko, T. M. 1 Zhuk, Vladimir Vasil’evich all top 5 Cited in 31 Serials 30 Journal of Approximation Theory 17 Ukrainian Mathematical Journal 6 Constructive Approximation 4 Mathematical Notes 4 Acta Mathematica Hungarica 4 Journal of Mathematical Sciences (New York) 3 Journal of Mathematical Analysis and Applications 3 Results in Mathematics 3 Computational Methods and Function Theory 2 Journal of Econometrics 2 Analysis and Mathematical Physics 1 Analysis Mathematica 1 Computers & Mathematics with Applications 1 Journal of Computational and Applied Mathematics 1 Numerical Functional Analysis and Optimization 1 Revista de la Unión Matemática Argentina 1 The Journal of Geometric Analysis 1 Numerical Algorithms 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Journal of Statistical Computation and Simulation 1 St. Petersburg Mathematical Journal 1 Turkish Journal of Mathematics 1 Positivity 1 Journal of Inequalities and Applications 1 Matematychni Studiï 1 Analysis in Theory and Applications 1 Proceedings of the Steklov Institute of Mathematics 1 Journal of Biological Dynamics 1 Journal of Electrical and Computer Engineering 1 Concrete Operators 1 SMAI Journal of Computational Mathematics all top 5 Cited in 17 Fields 79 Approximations and expansions (41-XX) 17 Functions of a complex variable (30-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 7 Real functions (26-XX) 4 Functional analysis (46-XX) 4 Numerical analysis (65-XX) 3 Statistics (62-XX) 1 History and biography (01-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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