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Positivity

, Volume 23, Issue 1, pp 1–10 | Cite as

Statistical equi-equal convergence of positive linear operators

  • Fadime DirikEmail author
  • Pınar Okçu Şahin
Article
  • 82 Downloads

Abstract

Many researchers have been interested in the concept of statistical convergence because of the fact that it is stronger than the classical convergence. Also, the concepts of statistical equal convergence and equi-statistical convergence are more general than the statistical uniform convergence. In this paper we define a new type of statistical convergence by using the notions of equi-statistical convergence and statistical equal convergence to prove a Korovkin type theorem. We show that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems which were demonstrated by earlier authors. After, we present an example in support of our definition and result presented in this paper. Finally, we also compute the rates of statistical equi-equal convergence of sequences of positive linear operators.

Keywords

Statistical equal convergence Equi-statistical convergence Positive linear operators Korovkin theorem Modulus of continuity 

Mathematics Subject Classification

41A25 41A36 

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsSinop UniversitySinopTurkey

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