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. Preprints2019, 2019120134. https://doi.org/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. https://doi.org/10.20944/preprints201912.0134.v1
Mursaleen, M.; Nasiruzzaman, M.; Kilicman, A.; Sapar, S.H. Dunkl generalization of Phillips operators and approximation in weighted spaces. Preprints2019, 2019120134. https://doi.org/10.20944/preprints201912.0134.v1
APA Style
Mursaleen, M., Nasiruzzaman, M., Kilicman, A., & Sapar, S.H. (2019). Dunkl generalization of Phillips operators and approximation in weighted spaces. Preprints. https://doi.org/10.20944/preprints201912.0134.v1
Chicago/Turabian Style
Mursaleen, M., Adem Kilicman and Siti Hasana Sapar. 2019 "Dunkl generalization of Phillips operators and approximation in weighted spaces" Preprints. https://doi.org/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.
Keywords
Szasz operator; Dunkl analogue; generalization of exponential function; Korovkin type theorem; modulus of continuity; order of convergence.
Subject
Computer Science and Mathematics, Analysis
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.