Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 915–934

# q-Szász–Durrmeyer Type Operators Based on Dunkl Analogue

• Abdul Wafi
• Ana Maria Acu
Article

## Abstract

The aim of present article is to introduce the q-Szász–Durrmeyer operators based on Dunkl analogue. We gave basic estimates with the help of q-calculus and then discussed basic convergence theorems. Next, we studied pointwise approximation results in terms of Peetre’s K-functional, second order modulus of continuity, Lipschitz type space and s th order Lipschitz type maximal function. Lastly, weighted approximation results and statistical approximation theorems are proved.

## Keywords

Dunkl analogue q-integers Szász operator Modulus of continuity

## Mathematics Subject Classification

41A25 41A30 41A35 41A36

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