Generalized weighted statistical convergence and application

Abstract

The object of this paper is to introduce the concepts of weighted lambda-statistical convergence and statistical summability ((N) over bar (lambda), p). We also establish some inclusion relations and some related results for these new summability methods. Further, we determine a Korovkin type approximation theorem through statistical summability ((N) over bar (lambda), p) and we show that our approximation theorem is stronger than classical Korovkin theorem by using classical Bernstein polynomials. (C) 2013 Elsevier Inc. All rights reserved.