# Nearly Coconvex Approximation

Serdica Mathematical Journal (2002)

- Volume: 28, Issue: 4, page 361-378
- ISSN: 1310-6600

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topLeviatan, 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 -

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