On shape parameter α -based approximation properties and q-statistical convergence of Baskakov-Gamma operators
We construct a novel family of summation-integral-type hybrid operators in terms of shape parameter α ∈ [0, 1] in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approxima...
| Main Authors: | , , , , |
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| Format: | Article |
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Hindawi
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/102384/ |
| _version_ | 1848863788922568704 |
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| author | Chen, Ming Yu Md Nasiruzzaman Mursaleen, Mohammad Ayman Rao, Nadeem Kilicman, Adem |
| author_facet | Chen, Ming Yu Md Nasiruzzaman Mursaleen, Mohammad Ayman Rao, Nadeem Kilicman, Adem |
| author_sort | Chen, Ming Yu |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We construct a novel family of summation-integral-type hybrid operators in terms of shape parameter α ∈ [0, 1] in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approximation findings for these sequences of positive linear operators utilising Peetre’s K-functional, Lipschitz class, and second-order modulus of smoothness. The approximation results are then obtained in weighted space. Finally, for these operators q-statistical convergence is also investigated. |
| first_indexed | 2025-11-15T13:38:29Z |
| format | Article |
| id | upm-102384 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:38:29Z |
| publishDate | 2022 |
| publisher | Hindawi |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1023842023-06-08T02:13:22Z http://psasir.upm.edu.my/id/eprint/102384/ On shape parameter α -based approximation properties and q-statistical convergence of Baskakov-Gamma operators Chen, Ming Yu Md Nasiruzzaman Mursaleen, Mohammad Ayman Rao, Nadeem Kilicman, Adem We construct a novel family of summation-integral-type hybrid operators in terms of shape parameter α ∈ [0, 1] in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approximation findings for these sequences of positive linear operators utilising Peetre’s K-functional, Lipschitz class, and second-order modulus of smoothness. The approximation results are then obtained in weighted space. Finally, for these operators q-statistical convergence is also investigated. Hindawi 2022-04-30 Article PeerReviewed Chen, Ming Yu and Md Nasiruzzaman and Mursaleen, Mohammad Ayman and Rao, Nadeem and Kilicman, Adem (2022) On shape parameter α -based approximation properties and q-statistical convergence of Baskakov-Gamma operators. Journal of Mathematics, 2022. art. no. 4190732. pp. 1-11. ISSN 2314-4629; ESSN: 2314-4785 https://www.hindawi.com/journals/jmath/2022/4190732/ 10.1155/2022/4190732 |
| spellingShingle | Chen, Ming Yu Md Nasiruzzaman Mursaleen, Mohammad Ayman Rao, Nadeem Kilicman, Adem On shape parameter α -based approximation properties and q-statistical convergence of Baskakov-Gamma operators |
| title | On shape parameter α -based approximation properties and q-statistical convergence of Baskakov-Gamma operators |
| title_full | On shape parameter α -based approximation properties and q-statistical convergence of Baskakov-Gamma operators |
| title_fullStr | On shape parameter α -based approximation properties and q-statistical convergence of Baskakov-Gamma operators |
| title_full_unstemmed | On shape parameter α -based approximation properties and q-statistical convergence of Baskakov-Gamma operators |
| title_short | On shape parameter α -based approximation properties and q-statistical convergence of Baskakov-Gamma operators |
| title_sort | on shape parameter α -based approximation properties and q-statistical convergence of baskakov-gamma operators |
| url | http://psasir.upm.edu.my/id/eprint/102384/ http://psasir.upm.edu.my/id/eprint/102384/ http://psasir.upm.edu.my/id/eprint/102384/ |