Generalized weighted statistical convergence and application

Abstract

The object of this paper is to introduce the concepts of weighted λ-statistical convergence and statistical summability (N¯λ,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¯λ,p) and we show that our approximation theorem is stronger than classical Korovkin theorem by using classical Bernstein polynomials.