Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators
Abstract In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-06-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02639-2 |
| _version_ | 1819088864931741696 |
|---|---|
| author | Shahid Ahmad Wani M. Mursaleen Kottakkaran Sooppy Nisar |
| author_facet | Shahid Ahmad Wani M. Mursaleen Kottakkaran Sooppy Nisar |
| author_sort | Shahid Ahmad Wani |
| collection | DOAJ |
| description | Abstract In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also considered. Finally, the Voronovskaya type theorem is demonstrated for some particular case of these polynomials. |
| first_indexed | 2024-12-21T21:58:49Z |
| format | Article |
| id | doaj.art-d10e963163bd43f2aeadebc800b92f10 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-21T21:58:49Z |
| publishDate | 2021-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d10e963163bd43f2aeadebc800b92f102022-12-21T18:48:53ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-06-012021111610.1186/s13660-021-02639-2Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operatorsShahid Ahmad Wani0M. Mursaleen1Kottakkaran Sooppy Nisar2Department of CSE, North Campus, University of KashmirDepartment of Medical Research, China Medical University Hospital, China Medical University (Taiwan)Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz UniversityAbstract In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also considered. Finally, the Voronovskaya type theorem is demonstrated for some particular case of these polynomials.https://doi.org/10.1186/s13660-021-02639-2Szasz operatorsBrenke type polynomialsJakimovski–Leviatan operatorsModulus of continuityWeighted space |
| spellingShingle | Shahid Ahmad Wani M. Mursaleen Kottakkaran Sooppy Nisar Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators Journal of Inequalities and Applications Szasz operators Brenke type polynomials Jakimovski–Leviatan operators Modulus of continuity Weighted space |
| title | Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators |
| title_full | Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators |
| title_fullStr | Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators |
| title_full_unstemmed | Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators |
| title_short | Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators |
| title_sort | certain approximation properties of brenke polynomials using jakimovski leviatan operators |
| topic | Szasz operators Brenke type polynomials Jakimovski–Leviatan operators Modulus of continuity Weighted space |
| url | https://doi.org/10.1186/s13660-021-02639-2 |
| work_keys_str_mv | AT shahidahmadwani certainapproximationpropertiesofbrenkepolynomialsusingjakimovskileviatanoperators AT mmursaleen certainapproximationpropertiesofbrenkepolynomialsusingjakimovskileviatanoperators AT kottakkaransooppynisar certainapproximationpropertiesofbrenkepolynomialsusingjakimovskileviatanoperators |