Operator version of Korovkin Theorem; Degree of Convergence and its Applications
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913238068756480 |
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| author | Kumar, V. B. Kiran Vinaya, P. C. |
| author_facet | Kumar, V. B. Kiran Vinaya, P. C. |
| contents | In a recent article, Dumitru Popa proved an operator version of the Korovkin theorem. We recall the quantitative version of the Korovkin theorem obtained by O. Shisha and B. Mond in 1968. In this paper, we obtain a quantitative estimate for the operator version of the Korovkin theorem obtained by Dumitru Popa. We also consider various examples where the operator version is applicable and obtain similar estimates leading to the degree of convergence. In addition, we obtain the trigonometric analogue of this result by proving the quantitative version. Finally, we apply this result to the preconditioning problem of large linear systems with the Toeplitz structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03154 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Operator version of Korovkin Theorem; Degree of Convergence and its Applications Kumar, V. B. Kiran Vinaya, P. C. Functional Analysis Classical Analysis and ODEs 41A36, 47B35 In a recent article, Dumitru Popa proved an operator version of the Korovkin theorem. We recall the quantitative version of the Korovkin theorem obtained by O. Shisha and B. Mond in 1968. In this paper, we obtain a quantitative estimate for the operator version of the Korovkin theorem obtained by Dumitru Popa. We also consider various examples where the operator version is applicable and obtain similar estimates leading to the degree of convergence. In addition, we obtain the trigonometric analogue of this result by proving the quantitative version. Finally, we apply this result to the preconditioning problem of large linear systems with the Toeplitz structure. |
| title | Operator version of Korovkin Theorem; Degree of Convergence and its Applications |
| topic | Functional Analysis Classical Analysis and ODEs 41A36, 47B35 |
| url | https://arxiv.org/abs/2207.03154 |