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arXiv · 1808.01817

Generalized Bernstein-Durrmeyer Operators of Blending Type

Arun Kajla·Meenu Goyal
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Abstract

In this article we present the Durrmeyer variant of generalized Bernstein operators that preserve the constant functions involving non-negative parameter ?. We derive the approximation behaviour of these operators including global approximation theorem via Ditzian-Totik modulus of continuity, the order of convergence for the Lipschitz type space. Furthermore, we study a Voronovskaja type asymptotic formula and local approximation theorem by means of second order modulus of smoothness. Furthermore, we obtain the rate of approximation for absolutely continuous functions having a derivative equivalent with a function of bounded variation. In the last section of the article, we illustrate the convergence of these operators for certain functions using Maple software.

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Arun Kajla, Meenu Goyal. 2018-08-06. Generalized Bernstein-Durrmeyer Operators of Blending Type. https://arxiv.org/abs/1808.01817

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