Shape-preserving approximation inL
p |
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Authors: | D Leviatan V Operstein |
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Institution: | 1. School of Mathematics Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel 2. Department of Mathematics Technion, Israel Institute of Technology, 32000, Haifa, Israel
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Abstract: | We prove a direct theorem for shape preservingL
p
-approximation, 0p, in terms of the classical modulus of smoothnessw
2(f, t
p
1
). This theorem may be regarded as an extension toL
p
of the well-known pointwise estimates of the Timan type and their shape-preserving variants of R. DeVore, D. Leviatan, and X. M. Yu. It leads to a characterization of monotone and convex functions in Lipschitz classes (and more general Besov spaces) in terms of their approximation by algebraic polynomials.Communicated by Ron DeVore. |
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Keywords: | AMS classification" target="_blank">AMS classification 41A10 41A25 41A29 |
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