Statistical weighted A-summability with application to Korovkin’s type approximation theorem

Abstract

Abstract We introduce the notion of statistical weighted A-summability of a sequence and establish its relation with weighted A-statistical convergence. We also define weighted regular matrix and obtain necessary and sufficient conditions for the matrix A to be weighted regular. As an application, we prove the Korovkin type approximation theorem through statistical weighted A-summability and using the BBH operator to construct an illustrative example in support of our result.

Keywords

• statistical convergence
• statistical weighted A-summability
• regular matrix
• positive linear operator
• Korovkin theorem