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Complex Analysis and Operator Theory

, Volume 12, Issue 7, pp 1519–1536 | Cite as

Szász-Durrmeyer Operators Based on Dunkl Analogue

  • Abdul Wafi
  • Nadeem Rao
Article

Abstract

In this article, we construct Sz\(\acute{a}\)sz-Durrmeyer type operators based on Dunkl analogue. We investigate several approximation results by these positive linear sequences, e.g. rate of convergence by means of classical modulus of continuity, uniform approximation using Korovkin type theorem on compact interval. Further, we discuss local approximations in terms of second order modulus of continuity, Peetre’s K-functional, Lipschitz type class and rth order Lipschitz-type maximal function. Weighted approximation and statistical approximation results are discussed in the last of this article.

Keywords

Sz\(\acute{a}\)sz operators Linear positive operators Modulus of continuity Rate of convergence Dunkl analogue 

Mathematics Subject Classification

41A10 41A25 41A28 41A35 41A36 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Department of MathematicsJamia Millia IslamiaNew DelhiIndia

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