A generalization of Phillips operators by using the Appell polynomials of class A ( 2 ) $A^{(2)}$
Abstract The current paper discusses some important approximation properties of a new modification of the Phillips operators with the help of A ( 2 ) $A^{(2)}$ class Appell polynomials. Firstly, we present the convergence rate of our new operators by using modulus of continuity. Then we establish a...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03260-3 |
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| _version_ | 1823861510986792960 |
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| author | Melek Sofyalıoğlu Aksoy |
| author_facet | Melek Sofyalıoğlu Aksoy |
| author_sort | Melek Sofyalıoğlu Aksoy |
| collection | DOAJ |
| description | Abstract The current paper discusses some important approximation properties of a new modification of the Phillips operators with the help of A ( 2 ) $A^{(2)}$ class Appell polynomials. Firstly, we present the convergence rate of our new operators by using modulus of continuity. Then we establish a quantitative Voronovskaya-type asymptotic result. We also introduce Hermite polynomials and Gould–Hopper polynomials, which are more specific examples of Appell polynomials. |
| format | Article |
| id | doaj-art-dfcb45d2f9d04ef7ab2c668a2e457277 |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-dfcb45d2f9d04ef7ab2c668a2e4572772025-02-09T12:59:32ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-02-012025111310.1186/s13660-025-03260-3A generalization of Phillips operators by using the Appell polynomials of class A ( 2 ) $A^{(2)}$Melek Sofyalıoğlu Aksoy0Department of Mathematics, Polatlı Faculty of Science and Letters, Ankara Hacı Bayram Veli UniversityAbstract The current paper discusses some important approximation properties of a new modification of the Phillips operators with the help of A ( 2 ) $A^{(2)}$ class Appell polynomials. Firstly, we present the convergence rate of our new operators by using modulus of continuity. Then we establish a quantitative Voronovskaya-type asymptotic result. We also introduce Hermite polynomials and Gould–Hopper polynomials, which are more specific examples of Appell polynomials.https://doi.org/10.1186/s13660-025-03260-3Phillips operatorsAppell polynomialsVoronovskaya-type theorem |
| spellingShingle | Melek Sofyalıoğlu Aksoy A generalization of Phillips operators by using the Appell polynomials of class A ( 2 ) $A^{(2)}$ Journal of Inequalities and Applications Phillips operators Appell polynomials Voronovskaya-type theorem |
| title | A generalization of Phillips operators by using the Appell polynomials of class A ( 2 ) $A^{(2)}$ |
| title_full | A generalization of Phillips operators by using the Appell polynomials of class A ( 2 ) $A^{(2)}$ |
| title_fullStr | A generalization of Phillips operators by using the Appell polynomials of class A ( 2 ) $A^{(2)}$ |
| title_full_unstemmed | A generalization of Phillips operators by using the Appell polynomials of class A ( 2 ) $A^{(2)}$ |
| title_short | A generalization of Phillips operators by using the Appell polynomials of class A ( 2 ) $A^{(2)}$ |
| title_sort | generalization of phillips operators by using the appell polynomials of class a 2 a 2 |
| topic | Phillips operators Appell polynomials Voronovskaya-type theorem |
| url | https://doi.org/10.1186/s13660-025-03260-3 |
| work_keys_str_mv | AT meleksofyalıogluaksoy ageneralizationofphillipsoperatorsbyusingtheappellpolynomialsofclassa2a2 AT meleksofyalıogluaksoy generalizationofphillipsoperatorsbyusingtheappellpolynomialsofclassa2a2 |