Approximation by Sampling Durrmeyer Operators in Weighted Space of Functions

Abstract

The present article deals with local and global approximation behaviors of sampling Durrmeyer operators for functions belonging to weighted spaces of continuous functions. After giving some fundamental notations of sampling type approximation methods and presenting well definiteness of the operators on weighted spaces of functions, we examine pointwise and uniform convergence of the family of operators and determine the rate of convergence via weighted modulus of continuity. A quantitative Voronovskaja theorem is also proved in order to obtain rate of pointwise convergence and upper estimate for this convergence. The last section is devoted to some numerical evaluations of sampling Durrmeyer operators with suitable kernels.

Keywords:

• quantitative Voronovskaja theorem
• rate of convergence
• sampling Durrmeyer operators
• uniform convergence
• weighted spaces

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 41A25
• 41A05

Additional information

Funding

The all authors have been supported within TUBITAK (The Scientific and Technological Research Council of Turkey) 3501-Project 119F263.