Statistical Convergence with Respect to Power Series Methods and Applications to Approximation Theory. (4th April 2019)

• Record Type: Journal Article
• Authors: Ünver, Mehmet; Orhan, Cihan
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 5(2019)
• Page Start: 535
• Page End: 547
• Publication Date: 2019-04-04
• Subjects: Korovkin type approximation -- power series method -- statistical convergence -- strong convergence -- uniform integrability; Primary 40C15 -- 40F05 -- 40A35 -- Secondary 41A36; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1561467
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article we introduce the concepts of P p -statistical convergence and Pp -strong convergence that are introduced via power series methods. Introducing a new type of uniform integrability with the help of power series method we obtain a relationship between these concepts which is actually a characterization of the concept of Pp -strong convergence. As an application we give a Korovkin type approximation theorem by using Pp -statistical convergence and also present an example to illustrate that Pp -statistical approximation is stronger than uniform approximation.