Dunkl analogue of Szász-mirakjan operators of blending type

Abstract

In the present work, we construct a Dunkl generalization of the modified Szász-Mirakjan operators of integral form defined by Pǎltanea [1]. We study the approximation properties of these operators including weighted Korovkin theorem, the rate of convergence in terms of the modulus of continuity, second order modulus of continuity via Steklov-mean, the degree of approximation for Lipschitz class of functions and the weighted space. Furthermore, we obtain the rate of convergence of the considered operators with the aid of the unified Ditzian-Totik modulus of smoothness and for functions having derivatives of bounded variation.

Keywords

• linear positive operators
• szász-mirakjan operators
• unified ditzian-totik modulus of smoothness
• weighted spaces
• dunkl operator
• 41a10
• 41a25
• 41a28
• 41a35
• 41a36