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q-Szász–Durrmeyer Type Operators Based on Dunkl Analogue

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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.

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Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, New Delhi, 110025, India

    Nadeem Rao & Abdul Wafi

  2. Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, 550012, Sibiu, Romania

    Ana Maria Acu

Authors
  1. Nadeem Rao
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  2. Abdul Wafi
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  3. Ana Maria Acu
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Correspondence to Nadeem Rao.

Additional information

Communicated by ILWOO CHO.

This work is carried out with the support of UGC BSR fellowship.

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Rao, N., Wafi, A. & Acu, A.M. q-Szász–Durrmeyer Type Operators Based on Dunkl Analogue. Complex Anal. Oper. Theory 13, 915–934 (2019). https://doi.org/10.1007/s11785-018-0816-3

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