Korovkin type approximation theorems for weighted αβ-statistical convergence

Abstract

The concept of αβ-statistical convergence was introduced and studied by Aktuuglu (Korovkin type approximation theorems proved via αβ-statistical conver- gence, J Comput Appl Math 259:174-181, 2014). In this work, we generalize the concept of αβ-statistical convergence and introduce the concept of weighted αβ- statistical convergence of order γ, weighted αβ-summability of order γ, and strongly weighted αβ-summable sequences of order γ. We also establish some inclusion rela- tion, and some related results for these new summability methods. Furthermore, we prove Korovkin type approximation theorems through weighted αβ-statistical conver- gence and apply the classical Bernstein operator to construct an example in support of our result.