Coconvex approximation in the uniform norm: the final frontier |
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| Authors: | K. Kopotun D. Leviatan I. A. Shevchuk |
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| Affiliation: | (1) Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada;(2) School of Mathematical Sciences, Raymond and Beverley Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel;(3) Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, 01033 Kyiv, Ukraine |
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| Abstract: | Summary The paper deals with approximation of a continuous function, on a finite interval, which changes convexity finitely many times, by algebraic polynomials which are coconvex with it. We give final answers to open questions concerning the validity of Jackson type estimates involving the weighted Ditzian-Totik moduli of smoothness. |
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| Keywords: | degree of approximation coconvex approximation by polynomials |
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