Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

Abstract

Purpose of this article is to introduce a modification of Phillips operators on the interval 1 2 , ∞ via Dunkl generalization. This type of modification enables to provide an error estimation on the interval 1 2 , ∞ . We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's K-functional and second order modulus of continuity.