Generalized weighted statistical convergence and application. (English) Zbl 1308.40003
Summary: The object of this paper is to introduce the concepts of weighted \(\lambda\)-statistical convergence and statistical summability \((\bar{N}_\lambda, p)\). 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 \((\bar{N}_\lambda, p)\) and we show that our approximation theorem is stronger than the classical Korovkin theorem by using classical Bernstein polynomials.
Keywords:
density; weighted mean; statistical convergence; Korovkin theorem; positive linear operatorReferences:
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