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Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/511

Title: Nearly Coconvex Approximation
Authors: Leviatan, D.
Shevchuk, I.
Keywords: Nearly Coconvex Approximation
Polynomial Approximation
Piecewise Polynomial Approximation
Jackson Estimates
Issue Date: 2002
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 28, No 4, (2002), 361p-378p
Abstract: Let f ∈ C[−1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials, and by piecewise polynomials, which are nearly coconvex with it, namely, polynomials and piecewise polynomials that preserve the convexity of f except perhaps in some small neighborhoods of the points where f changes its convexity. We obtain Jackson type estimates and summarize the positive and negative results in a truth-table as we have previously done for nearly comonotone approximation.
Description: * Part of this work was done while the second author was on a visit at Tel Aviv University in March 2001
URI: http://hdl.handle.net/10525/511
ISSN: 1310-6600
Appears in Collections:Volume 28 Number 4

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