Approximation Theorems for Generalized Complex Kantorovich-Type Operators

Abstract EN

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|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.