Generalized Kantorovich type Sza'sz-Mirakjan operators based on q-integers

Abstract

In this paper, we introduce a new type Kantorovich variant of Szasz-Mirakjan operators based on q-integers. We study convergence properties by using Korovkin's theorem and estimate the rate of convergence by using modulus of continuity. We examine local and weighted approximation properties in terms of modulus of continuity. We obtain a direct estimate in terms of Lipschitz type maximal function of order alpha. Moreover, we give a quantitative Voronovskaja type theorem for these newly defined operators. Finally, we present numerical results and graphical representation.