On modified Dunkl generalization of Szász operators via q-calculus

Abstract

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 [ 1 2 , ∞ ) $[\frac{1}{2},\infty)$ 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

• q-integers
• Dunkl analogue
• Szász operator
• q-Szász-Mirakjan-Kantorovich
• modulus of continuity
• Peetre’s K-functional