Citation
Mursaleen, Mohammad and Nasiruzzaman, Mohammad and Kilicman, Adem and Sapar, Siti Hasana
(2020)
Dunkl generalization of Phillips operators and approximation in weighted spaces.
Advances in Difference Equations, 2020.
art. no. 365.
pp. 1-15.
ISSN 1687-1839; ESSN: 1687-1847
Abstract
The purpose of this article is to introduce a modification of Phillips operators on the interval [12,∞) via a Dunkl generalization. We further define the Stancu type generalization of these operators as S∗n,υ(f;x)=n2eυ(nχn(x))∑∞ℓ=0(nχn(x))ℓγυ(ℓ)∫∞0e−ntnℓ+2υθℓ−1tℓ+2υθℓγυ(ℓ)f(nt+αn+β)dt, f∈Cζ(R+), and calculate their moments and central moments. We discuss the convergence results via Korovkin type and weighted Korovkin type theorems. Furthermore, we calculate the rate of convergence by means of the modulus of continuity, Lipschitz type maximal functions, Peetre’s K-functional and the second order modulus of continuity.
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Institute for Mathematical Research |
| DOI Number: | https://doi.org/10.1186/s13662-020-02820-9 |
| Publisher: | Springer |
| Keywords: | Szász operator; Dunkl analogue; Generalization of exponential function; Korovkin type theorem; Modulus of continuity; Order of convergence |
| Depositing User: | Ms. Nuraida Ibrahim |
| Date Deposited: | 22 Dec 2021 08:54 |
| Last Modified: | 22 Dec 2021 08:54 |
| Altmetrics: | http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1186/s13662-020-02820-9 |
| URI: | http://psasir.upm.edu.my/id/eprint/88536 |
| Statistic Details: | View Download Statistic |
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