Original scientific paper

Approximation for periodic functions via statistical σ-convergence

Kamil Demirci ; Department of Mathematics, Faculty of Arts and Sciences, Sinop University, Sinop, Turkey
Fadime Dirik ; Department of Mathematics, Faculty of Arts and Sciences, Sinop University, Sinop, Turkey

Abstract

In this study, using the concept of statistical σ-convergence which is stronger than convergence and statistical convergence we prove a
Korovkin-type approximation theorem for sequences of positive linear
operators defined on $C^{\ast }$ which is the space of all $2\pi $-periodic and continuous functions on $\mathbb{R}$, the set of all real numbers. We also study the rates of statistical σ-convergence of approximating positive linear operators.

Keywords

statistical convergence; statistical σ-convergence; positive linear operator; Korovkin-type approximation theorem; periodic functions; Fejer polynomials

Hrčak ID:

68624

URI

https://hrcak.srce.hr/68624

Publication date:

10.6.2011.

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