Approximation Properties of the Modified Stancu Operators. (4th March 2017)

• Record Type: Journal Article
• Authors: Acu, Ana Maria; Agrawal, P. N.; Neer, Trapti
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 3(2017)
• Page Start: 279
• Page End: 292
• Publication Date: 2017-03-04
• Subjects: Ditzian-Totik modulus of smoothness -- rate of convergence -- Stancu operator -- Voronovskaja type theorem; 41A36 -- 41A25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1248564
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article we construct a sequence of Stancu-type operators that are based on a function τ . This function is any function on [0, 1] continuously differentiable ∞ times, such that τ (0) = 0, τ (1) = 1 and τ ′ ( x )>0 for x ∈[0, 1]. Note that the Korovkin set is generalized to {1, τ, τ 2 } and these operators present a better degree of approximation then the original ones. We give a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem.