Statistical αβ−Summability and Korovkin Type Approximation Theorem

Abstract

In this study, we define $[N^{\gamma},
\alpha\beta]_{q}-$summability and statistical
$(N^{\gamma},\alpha\beta)$ summability. We also establish some
inclusion relation and some related results for this new
summability methods. Further we apply Korovkin type approximation
theorem through statistical $(N^{\gamma},\alpha\beta)$ summability
and we apply the classical Bernstein operator to construct an
example in support of our result. Furthermore, we present a rate of
convergence which is uniform in Korovkin type theorem by statistical
$(N^{\gamma},\alpha\beta)$ summability.