Approximation properties of weighted Kantorovich type operators in compact disks

Abstract

In this paper, we discuss the approximation properties of the complex weighted Kantorovich type operators. Quantitative estimates of the convergence, the Voronovskaja type theorem, and saturation of convergence for complex weighted Kantorovich polynomials attached to analytic functions in compact disks will be given. In particular, we show that for functions analytic in {z is an element of C : vertical bar z vertical bar < R}, the rate of approximation by the weighted complex Kantorovich type operators is 1/n.