Weighted statistical convergence and its application to Korovkin type approximation theorem


Mursaleen M., Karakaya V. , Erturk M. , Gursoy F.

APPLIED MATHEMATICS AND COMPUTATION, vol.218, no.18, pp.9132-9137, 2012 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 218 Issue: 18
  • Publication Date: 2012
  • Doi Number: 10.1016/j.amc.2012.02.068
  • Title of Journal : APPLIED MATHEMATICS AND COMPUTATION
  • Page Numbers: pp.9132-9137
  • Keywords: Density, Statistical convergence, Weighted statistical convergence, Statistical summability ((N)over-bar, p(n)), Positive linear operator, Korovkin type approximation theorem, SUMMABILITY

Abstract

The concept of weighted statistical convergence was introduced and studied by Karakaya and Chishti (2009) [7]. In this paper, we modify the definition of weighted statistical convergence and find its relationship with the concept of statistical summability ((N) over bar, p(n)) due to Moricz and Orhan (2004) [10]. We apply this new summability method to prove a Korovkin type approximation theorem by using the test functions 1, e(-x), e(-2x). We apply the classical Baskakov operator to construct an example in support of our result. (C) 2012 Elsevier Inc. All rights reserved.