Rate of convergence by Kantorovich-Szász type operators based on Brenke type polynomials

J Inequal Appl. 2017;2017(1):156. doi: 10.1186/s13660-017-1430-z. Epub 2017 Jun 29.

Abstract

The present paper deals with the approximation properties of the univariate operators which are the generalization of the Kantorovich-Szász type operators involving Brenke type polynomials. We investigate the order of convergence by using Peetre's K-functional and the Ditzian-Totik modulus of smoothness and study the degree of approximation of the univariate operators for continuous functions in a Lipschitz space, a Lipschitz type maximal function and a weighted space. The rate of approximation of functions having derivatives equivalent with a function of bounded variation is also obtained.

Keywords: Brenke type polynomials; Ditzian-Totik modulus of smoothness; Peetre’s K-functional; Szász operator; derivative of bounded variation; rate of convergence.