Approximation Theorems for Generalized Complex Kantorovich-Type Operators

Abstract

The order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials (q > 0) attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in {z is an element of C : vertical bar z vertical bar < R}, R > q, the rate of approximation by the q-Kantorovich operators (q > 1) is of order q(n) versus 1/n for the classical Kantorovich operators.