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
