On statistical convergence of difference sequences of fractional order and related Korovkin type approximation theorems


Baliarsingh P., Kadak U., Mursaleen M.

QUAESTIONES MATHEMATICAE, vol.41, no.8, pp.1117-1133, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 8
  • Publication Date: 2018
  • Doi Number: 10.2989/16073606.2017.1420705
  • Title of Journal : QUAESTIONES MATHEMATICAE
  • Page Numbers: pp.1117-1133

Abstract

Prior to investigating on sequence spaces and their convergence, we study the notion of statistical convergence of difference sequences of fractional order alpha is an element of Double-struck capital R. As generalizations of previous works, this study includes several special cases under different limiting conditions of alpha, such as the notion of statistical convergence of difference sequences of zeroth and mth (integer) order. In fact, we study certain new results on statistical convergence via the difference operator Delta(alpha) and interpret them to those of previous works. Also, by using the convergence of Delta(alpha)-summable sequences which is stronger than statistical convergence of difference sequences, we apply classical Bernstein operator and a generalized form of Meyer-Konig and Zeller operator to construct an example in support of our result. Also, we study the rates of Delta(alpha)-statistical convergence of positive linear operators.