General Summability Methods in the Approximation by Bernstein–Chlodovsky Operators. (4th June 2021)

• Record Type: Journal Article
• Authors: Alemdar, Meryem Ece; Duman, Oktay
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 5(2021)
• Page Start: 497
• Page End: 509
• Publication Date: 2021-06-04
• Subjects: Bernstein–Chlodovsky operators -- Cesàro summability -- modulus of continuity -- summability methods; 41A36 -- 41A25 (primary) -- and 40A05 -- 40A25 (secondary); Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1895831
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, by using regular summability methods we modify the Bernstein–Chlodovsky operators in order get more general and powerful results than the classical aspects. We study Korovkin-type approximation theory on weighted spaces. As a special case, it is possible to Cesàro approximate (arithmetic mean convergence) to the test function e 2 ( x ) = x 2 although it fails for the classical Bernstein–Chlodovsky operators. At the end of the paper, we extend our results to the multi-dimensional case.