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

The present paper deals with the approximation properties of the univariate operators which are the generalization of the Kantorovich-Szasz 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.