Szasz-Durrmeyer Operators Based on Dunkl Analogue

摘要

In this article, we construct Szasz-Durrmeyer type operators based on Dunkl analogue. We investigate several approximation results by these positive linear sequences, e.g. rate of convergence by means of classical modulus of continuity, uniform approximation using Korovkin type theorem on compact interval. Further, we discuss local approximations in terms of second order modulus of continuity, Peetre's K-functional, Lipschitz type class and r th order Lipschitz-type maximal function. Weighted approximation and statistical approximation results are discussed in the last of this article.