Grüss and Grüss-Voronovskaya-type estimates for complex convolution polynomial operators

Abstract

The aim of this paper is to obtain Grüss and Grüss-Voronovskaya inequalities with exact quantitativeestimates (with respect to the degree) for the complex convolution polynomial operators of de la Vallée Poussin, ofZygmund-Riesz and of Jackson, acting on analytic functions.Keywords: Complex convolution polynomials, de la Vallée-Poussin kernel, Riesz-Zygmund kernel, Jackson kernel,Grüss-type estimate, Grüss-Voronovskaya-type estimate, analytic functions.