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 ApproximationPolynomial ApproximationPiecewise Polynomial ApproximationJackson 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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