On the Convergence of Bernstein-Stancu Polynomials in the Variation Seminorm. (2nd February 2016)

• Record Type: Journal Article
• Authors: Öksüzer, Özlem; Karsli, Harun; Yeşildal, Fatma Taşdelen
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 5(2016)
• Page Start: 583
• Page End: 602
• Publication Date: 2016-02-02
• Subjects: Bernstein-Stancu polynomials -- convergence in variation seminorm -- variation detracting property -- Voronovskaya-type theorems; 41A25 -- 41A35; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2015.1137938
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: This article studies the variation detracting property and rate of approximation of the Bernstein-Stancu polynomials in the space of functions of bounded variation with respect to the variation seminorm. Moreover, we will present Voronovskaya-type theorems for Bernstein-Stancu polynomials B n, α, β f and for the first derivative of these polynomials. Finally we include some graphical examples.