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Szász-Durrmeyer Operators Based on Dunkl Analogue

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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.

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Authors and Affiliations

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

    Abdul Wafi & Nadeem Rao

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  1. Abdul Wafi
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  2. Nadeem Rao
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Correspondence to Nadeem Rao.

Additional information

Communicated by David Kimsey.

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

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Wafi, A., Rao, N. Szász-Durrmeyer Operators Based on Dunkl Analogue. Complex Anal. Oper. Theory 12, 1519–1536 (2018). https://doi.org/10.1007/s11785-017-0647-7

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