Trigonometric derived rate of convergence of various smooth singular integral operators
In this article, we continue the study of approximation of various smooth singular integral operators. This time the foundation of our research is a trigonometric Taylor’s formula. We establish the convergence of our operators to the unit operator with rates via Jackson type inequalities engaging th...
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| Format: | Article |
| Language: | English |
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Tuncer Acar
2024-01-01
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| Series: | Modern Mathematical Methods |
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| Online Access: | https://modernmathmeth.com/index.php/pub/article/view/22 |
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| author | George Anastassiou |
| author_facet | George Anastassiou |
| author_sort | George Anastassiou |
| collection | DOAJ |
| description | In this article, we continue the study of approximation of various smooth singular integral operators. This time the foundation of our research is a trigonometric Taylor’s formula. We establish the convergence of our operators to the unit operator with rates via Jackson type inequalities engaging the first modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not positive. Our results are pointwise and uniform. The studied operators here are of the following types: Gauss-Weierstrass, Poisson-Cauchy and trigonometric. |
| format | Article |
| id | doaj-art-7ce55b06a01a4ffba53bc0ac934d8935 |
| institution | OA Journals |
| issn | 3023-5294 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Tuncer Acar |
| record_format | Article |
| series | Modern Mathematical Methods |
| spelling | doaj-art-7ce55b06a01a4ffba53bc0ac934d89352025-08-20T02:15:59ZengTuncer AcarModern Mathematical Methods3023-52942024-01-0121274022Trigonometric derived rate of convergence of various smooth singular integral operatorsGeorge Anastassiou0https://orcid.org/0000-0002-3781-9824University of Memphis, Department of Mathematical Sciences, Memphis, Tn 38152, USAIn this article, we continue the study of approximation of various smooth singular integral operators. This time the foundation of our research is a trigonometric Taylor’s formula. We establish the convergence of our operators to the unit operator with rates via Jackson type inequalities engaging the first modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not positive. Our results are pointwise and uniform. The studied operators here are of the following types: Gauss-Weierstrass, Poisson-Cauchy and trigonometric.https://modernmathmeth.com/index.php/pub/article/view/22singular integralgauss-weierstrasspoisson-cauchy and trigonometric operatormodulus of continuitytrigonometric taylor formula |
| spellingShingle | George Anastassiou Trigonometric derived rate of convergence of various smooth singular integral operators Modern Mathematical Methods singular integral gauss-weierstrass poisson-cauchy and trigonometric operator modulus of continuity trigonometric taylor formula |
| title | Trigonometric derived rate of convergence of various smooth singular integral operators |
| title_full | Trigonometric derived rate of convergence of various smooth singular integral operators |
| title_fullStr | Trigonometric derived rate of convergence of various smooth singular integral operators |
| title_full_unstemmed | Trigonometric derived rate of convergence of various smooth singular integral operators |
| title_short | Trigonometric derived rate of convergence of various smooth singular integral operators |
| title_sort | trigonometric derived rate of convergence of various smooth singular integral operators |
| topic | singular integral gauss-weierstrass poisson-cauchy and trigonometric operator modulus of continuity trigonometric taylor formula |
| url | https://modernmathmeth.com/index.php/pub/article/view/22 |
| work_keys_str_mv | AT georgeanastassiou trigonometricderivedrateofconvergenceofvarioussmoothsingularintegraloperators |