Approximation properties on q -Szasz-Mirakjan-Kantrovich Stancu type operators via Dunkl generalization

Abstract

This paper is devoted to study the approximation properties and rate of approximation of the Szasz-Mirakjan-Kantrovich-Stancu type polynomials generated by the Dunkl generalization of the exponential function with respect to q -calculus. We present approximation properties with the help of well-known Korovkin's theorem and determine the rat e of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K-functional, and the second-order modulus of continuity. Moreover, we obtain the approximation results for Bivariate case for these operators