Title

Local Approximation By A Variant Of Bernstein-Durrmeyer Operators

Keywords

Approximation by positive operators; Asymptotic expansions; Degree of approximation; Functions of bounded variation; Rate of convergence; Sharp bound; Total variation

Abstract

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

Publication Date

6-1-2008

Publication Title

Nonlinear Analysis, Theory, Methods and Applications

Volume

68

Issue

11

Number of Pages

3372-3381

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.na.2007.03.026

Socpus ID

41949137863 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/41949137863

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