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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.

Statistical αβ-summability and Korovkin type approximation theorem