Preprint Article Version 1 This version is not peer-reviewed

Dunkl generalization of Phillips operators and approximation in weighted spaces

Version 1 : Received: 9 December 2019 / Approved: 10 December 2019 / Online: 10 December 2019 (14:58:47 CET)

How to cite: Mursaleen, M.; Nasiruzzaman, M.; Kilicman, A.; Sapar, S.H. Dunkl generalization of Phillips operators and approximation in weighted spaces. Preprints 2019, 2019120134 (doi: 10.20944/preprints201912.0134.v1). Mursaleen, M.; Nasiruzzaman, M.; Kilicman, A.; Sapar, S.H. Dunkl generalization of Phillips operators and approximation in weighted spaces. Preprints 2019, 2019120134 (doi: 10.20944/preprints201912.0134.v1).

Abstract

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.

Subject Areas

Szasz operator; Dunkl analogue; generalization of exponential function; Korovkin type theorem; modulus of continuity; order of convergence.

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