Title

Local approximation by a variant of Bernstein-Durrmeyer operators

Authors

Authors

U. Abel; V. Gupta;R. N. Mohapatra

Comments

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Abbreviated Journal Title

Nonlinear Anal.-Theory Methods Appl.

Keywords

approximation by positive operators; rate of convergence; degree of; approximation; functions of bounded variation; total variation; sharp; bound; asymptotic expansions; MEYER-KONIG; ASYMPTOTIC APPROXIMATION; ZELLER OPERATORS; BLEIMANN; BUTZER; HAHN; Mathematics, Applied; Mathematics

Abstract

This paper deals with the local approximation properties of a certain variant (M) over tilden of the Bernstein-Durrmeyer operators. Firstly, we obtain an estimate on the rate of convergence of (M) over tilden by means of the decomposition technique for functions of bounded variation. It will be shown that our estimate in its most convenient form (Corllary 2) is asymptotically optimal. Furthermore, we derive the complete asymptotic expansion for the sequence of the operators (M) over tilden as n tends to infinity. (C) 2007 Elsevier Ltd. All rights reserved.

Journal Title

Nonlinear Analysis-Theory Methods & Applications

Volume

68

Issue/Number

11

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

3372

Last Page

3381

WOS Identifier

WOS:000255809300012

ISSN

0362-546X

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