A class of Markov type operators which preserve ej,j⩾1

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摘要

In this paper we construct a class of Markov type operators which preserve ej,j⩾1. We give a recurrence relation for the moments of this operator and study the convergence. We show the uniform convergence of the derivative of order r⩾0 of the operator. A Voronovskaya formula and some inequalities are presented.

论文关键词：Markov type operators,Bernstein–Durrmeyer operator,Moments,Uniform convergence,Voronovskaya formula,Convex functions

论文评审过程：Available online 13 November 2014.

论文官网地址：https://doi.org/10.1016/j.amc.2014.10.078