On modified Dunkl generalization of Szász operators via q-calculus

J Inequal Appl. 2017;2017(1):38. doi: 10.1186/s13660-017-1311-5. Epub 2017 Feb 7.

Abstract

The purpose of this paper is to introduce a modification of q-Dunkl generalization of exponential functions. These types of operators enable better error estimation on the interval [Formula: see text] than the classical ones. We obtain some approximation results via a well-known Korovkin-type theorem and a weighted Korovkin-type theorem. Further, we obtain the rate of convergence of the operators for functions belonging to the Lipschitz class.

Keywords: Dunkl analogue; Peetre’s K-functional; Szász operator; modulus of continuity; q-Szász-Mirakjan-Kantorovich; q-integers.