Indian Journal of Industrial and Applied Mathematics
  • Year: 2019
  • Volume: 10
  • Issue: 1SI

Approximation of Periodic Functions via Statistical š“‘-summability and Its Applications to Approximation Theorems

1Department of Mathematics, Veer Surendra Sai University of Technology, Burla-768018, Odisha, India

2Department of Mathematics, Veer Surendra Sai University of Technology, Burla-768018, Odisha, India

3Department of Mathematics, National Institute of Science and Technology, Pallur Hills, Golanthara-761008, Odisha, India

(*Corresponding author) Email: *skpaikray math@vssut.ac.in

**bidumath.05@gmail.com

***umakanta misra@yahoo.com

Abstract

The A-statistical summability is stronger than A-statistical convergence which was introduced by Edely and Mursaleen [7] (see [Edely and Mursaleen, On statistical A-summability, Math. Comput. Model.49, 672ā€“680). In this paper, by using the concept of statistical š“‘-summability we establish a result on Korovkin-type approximation theorem for periodic functions defined on a Banach space Cāˆ—(š“”), which is also stronger than its statistical A-summability version. Furthermore, we demonstrate a theorem for the rate of the š“‘-statistical convergence for same set of functions with the help of the modulus of continuity.

Keywords

Primary 40A05, 41A36, Secondary 40G15, Statistical š“‘-summability, statistical A-summability, š“‘-statistical convergence, rate of convergence, Korovkin type approximation theorem