Generalized Bernstein-Durrmeyer Operators of Blending Type
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.
Cite
@article{arxiv.1808.01817,
title = {Generalized Bernstein-Durrmeyer Operators of Blending Type},
author = {Arun Kajla and Meenu Goyal},
journal= {arXiv preprint arXiv:1808.01817},
year = {2018}
}