APPROXIMATION PROPERTIES OF MODIFIED KANTOROVICH TYPE (p, q)-BERNSTEIN OPERATORS

In the present paper, we construct modified Bernstein-Kantorovich operators by adding a parameter alpha and using new method and idea based on (p,q)-calculus. We establish the moments and the central moments of the operators. Then, we obtain a Korovkin type approximation theorem and discuss two local approximation theorems using Steklov mean and K-functional in terms of modulus of smoothness. Next, the rate of convergence on continuous function space, differentiable function space and Lipschitz function space are studied. Finally, Voronovskaja type theorem is also investigated.