Approximation by Sampling Durrmeyer Operators in Weighted Space of Functions. (27th July 2022)

• Record Type: Journal Article
• Authors: Alagoz, Osman; Turgay, Metin; Acar, Tuncer; Parlak, Merve
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 10(2022)
• Page Start: 1223
• Page End: 1239
• Publication Date: 2022-07-27
• Subjects: quantitative Voronovskaja theorem -- rate of convergence -- sampling Durrmeyer operators -- uniform convergence -- weighted spaces; 41A25 -- 41A05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2096630
• Languages: English
• ISSNs: 0163-0563

Abstract

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.