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 ∈ ℂ : | z | < 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.