Version 1
: Received: 11 March 2020 / Approved: 12 March 2020 / Online: 12 March 2020 (14:28:31 CET)
How to cite:
Mursaleen, M.; Nasiruzzaman, M.; Kilicman, A.; Sapar, S. H. Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces. Preprints2020, 2020030218. https://doi.org/10.20944/preprints202003.0218.v1
Mursaleen, M.; Nasiruzzaman, M.; Kilicman, A.; Sapar, S. H. Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces. Preprints 2020, 2020030218. https://doi.org/10.20944/preprints202003.0218.v1
Mursaleen, M.; Nasiruzzaman, M.; Kilicman, A.; Sapar, S. H. Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces. Preprints2020, 2020030218. https://doi.org/10.20944/preprints202003.0218.v1
APA Style
Mursaleen, M., Nasiruzzaman, M., Kilicman, A., & Sapar, S. H. (2020). Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces. Preprints. https://doi.org/10.20944/preprints202003.0218.v1
Chicago/Turabian Style
Mursaleen, M., Adem Kilicman and Siti Hasana Sapar. 2020 "Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces" Preprints. https://doi.org/10.20944/preprints202003.0218.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
Szász 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.