Local approximation by a variant of Bernstein-Durrmeyer operators

    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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