Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

M. Mursaleen; Md Nasiruzzaman; Adem Kilicman; Siti Hasana Sapar

doi:10.20944/preprints202003.0218.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 11 March 2020 / Approved: 12 March 2020 / Online: 12 March 2020 (14:28:31 CET)

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

Szász operator; dunkl analogue; generalization of exponential function; korovkin type theorem; modulus of continuity; order of convergence

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Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

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