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Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 915–934 | Cite as

q-Szász–Durrmeyer Type Operators Based on Dunkl Analogue

  • Nadeem RaoEmail author
  • 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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsJamia Millia IslamiaNew DelhiIndia
  2. 2.Department of Mathematics and InformaticsLucian Blaga University of SibiuSibiuRomania

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