Approximation properties of the new type generalized Bernstein-Kantorovich operators

In this paper, we introduce new type of generalized Kantorovich variant of $\alpha$-Bernstein operators and study their approximation properties. We obtain estimates of rate of convergence involving first and second order modulus of continuity and Lipschitz function are studied for these operators. Furthermore, we establish Voronovskaya type theorem of these operators. The last section is devoted to bivariate new type $\alpha$-Bernstein-Kantorovich operators and their approximation behaviors. Also, some graphical illustrations and numerical results are provided.