Kantorovich Type Generalization of Bernstein Type Rational Functions Based on (p,q)-Integers

Abstract

In this paper, we define a new Kantorovich-type (p,q)-generalization of the Balazs-Szabados operators. We derive a recurrence formula, and with the help of this formula, we give explicit formulas for the first and second-order moments, which follow a symmetric pattern. We estimate the second and fourth-order central moments. We examine the local approximation properties in terms of modulus of continuity, we give a Voronovskaja type theorem, and we give the weighted approximation properties of the operators.