WEIGHTED APPROXIMATION IN UNIFORM NORM BY MEYER-K¨ONIG AND ZELLER OPERATORS

TitleWEIGHTED APPROXIMATION IN UNIFORM NORM BY MEYER-K¨ONIG AND ZELLER OPERATORS
Publication TypeJournal Article
Year of Publication2017
AuthorsGadjev I, Parvanov P
JournalAnnuaire de l’Universite de Sofia “st. Kliment Ohridski” Faculte de Mathematiques et Informatique
Volume104
Pagination77-87
ISSN0205-0808
Keywordsdirect theorem, K-functional, Meyer-K¨onig and Zeller operator, strong converse theorem, weighted approximation.
Abstract

The weighted approximation errors of $Meyer-K\ddot{o}nig$ and $Zeller$ operator is characterized for weights of the form $w(x) = x^{\gamma_0}(1 − x)^{\gamma_1} $, where $\gamma_0 \in [−1, 0], \gamma_1 \in \mathbb{R}$. Direct inequalities and strong converse inequalities of type A are proved in terms of the weighted $K$-functional.

2000 MSC

41A36, 41A25, 41A27, 41A17

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