Smoothness Properties of Modified Bernstein-Kantorovich Operators. (2nd January 2016)

• Record Type: Journal Article
• Authors: Özarslan, Mehmet Ali; Duman, Oktay
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 1(2016)
• Page Start: 92
• Page End: 105
• Publication Date: 2016-01-02
• Subjects: Bernstein-Kantorovich operators -- Ditzian-Totik modulus of smoothness -- modulus of continuity -- simultaneous approximation; 41A36 -- 41A25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2015.1079219
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we consider modified Bernstein-Kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ones classically used. We obtain a simultaneous approximation result for our operators. Also, we prove two direct approximation results via the usual second-order modulus of smoothness and the second-order Ditzian-Totik modulus of smoothness, respectively. Finally, some graphical illustrations are provided.