Nearly Coconvex Approximation

Leviatan, D., and Shevchuk, I.. "Nearly Coconvex Approximation." Serdica Mathematical Journal 28.4 (2002): 361-378. <http://eudml.org/doc/11569>.

@article{Leviatan2002,
abstract = {* Part of this work was done while the second author was on a visit at Tel Aviv University in March 2001Let 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.},
author = {Leviatan, D., Shevchuk, I.},
journal = {Serdica Mathematical Journal},
keywords = {Nearly Coconvex Approximation; Polynomial Approximation; Piecewise Polynomial Approximation; Jackson Estimates; nearly coconvex approximation; polynomial approximation; piecewise polynomial approximation; Jackson estimates},
language = {eng},
number = {4},
pages = {361-378},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Nearly Coconvex Approximation},
url = {http://eudml.org/doc/11569},
volume = {28},
year = {2002},
}

TY - JOUR
AU - Leviatan, D.
AU - Shevchuk, I.
TI - Nearly Coconvex Approximation
JO - Serdica Mathematical Journal
PY - 2002
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 28
IS - 4
SP - 361
EP - 378
AB - * Part of this work was done while the second author was on a visit at Tel Aviv University in March 2001Let 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.
LA - eng
KW - Nearly Coconvex Approximation; Polynomial Approximation; Piecewise Polynomial Approximation; Jackson Estimates; nearly coconvex approximation; polynomial approximation; piecewise polynomial approximation; Jackson estimates
UR - http://eudml.org/doc/11569
ER -