Dunkl generalization of Phillips operators and approximation in weighted spaces
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...
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my.upm.eprints.885362021-12-22T08:54:31Z http://psasir.upm.edu.my/id/eprint/88536/ Dunkl generalization of Phillips operators and approximation in weighted spaces Mursaleen, Mohammad Nasiruzzaman, Mohammad Kilicman, Adem Sapar, Siti Hasana 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. Springer 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/88536/1/ABSTRACT.pdf 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 https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-020-02820-9 10.1186/s13662-020-02820-9 |
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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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Article |
author |
Mursaleen, Mohammad Nasiruzzaman, Mohammad Kilicman, Adem Sapar, Siti Hasana |
spellingShingle |
Mursaleen, Mohammad Nasiruzzaman, Mohammad Kilicman, Adem Sapar, Siti Hasana Dunkl generalization of Phillips operators and approximation in weighted spaces |
author_facet |
Mursaleen, Mohammad Nasiruzzaman, Mohammad Kilicman, Adem Sapar, Siti Hasana |
author_sort |
Mursaleen, Mohammad |
title |
Dunkl generalization of Phillips operators and approximation in weighted spaces |
title_short |
Dunkl generalization of Phillips operators and approximation in weighted spaces |
title_full |
Dunkl generalization of Phillips operators and approximation in weighted spaces |
title_fullStr |
Dunkl generalization of Phillips operators and approximation in weighted spaces |
title_full_unstemmed |
Dunkl generalization of Phillips operators and approximation in weighted spaces |
title_sort |
dunkl generalization of phillips operators and approximation in weighted spaces |
publisher |
Springer |
publishDate |
2020 |
url |
http://psasir.upm.edu.my/id/eprint/88536/1/ABSTRACT.pdf http://psasir.upm.edu.my/id/eprint/88536/ https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-020-02820-9 |
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