A Dunkl type generalization of Szász operators via post-quantum calculus

Abdullah Alotaibi; Md Nasiruzzaman; M Mursaleen

doi:10.1186/s13660-018-1878-5

A Dunkl type generalization of Szász operators via post-quantum calculus

J Inequal Appl. 2018;2018(1):287. doi: 10.1186/s13660-018-1878-5. Epub 2018 Oct 22.

Authors

Abdullah Alotaibi¹, Md Nasiruzzaman², M Mursaleen^{1

3}

Affiliations

¹ 1Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.
² 2Department of Computer Science (SEST), Jamia Hamdard, New Delhi, India.
³ 3Department of Mathematics, Aligarh Muslim University, Aligarh, India.

Abstract

The object of this paper to construct Dunkl type Szász operators via post-quantum calculus. We obtain some approximation results for these new operators and compute convergence of the operators by using the modulus of continuity. Furthermore, we obtain the rate of convergence of these operators for functions belonging to the Lipschitz class. We also study the bivariate version of these operators.

Keywords: ( p , q ) -analogues of the exponential function; ( p , q ) -integers; Dunkl analogue; Szász operator; modulus of continuity.