Approximation using Jakimovski–Leviatan operators of Durrmeyer type with 2D-Appell polynomials
Abstract This article delves into Jakimovski–Leviatan–Durrmeyer type operators based on 2D-Appell polynomials. The investigation initiates by exploring the Korovkin-type approximation theorem and its convergence rates, employing both the traditional modulus of continuity and a class of Lipschitz fun...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-04-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03300-y |
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| author | Manoj Kumar Nusrat Raza M. Mursaleen |
| author_facet | Manoj Kumar Nusrat Raza M. Mursaleen |
| author_sort | Manoj Kumar |
| collection | DOAJ |
| description | Abstract This article delves into Jakimovski–Leviatan–Durrmeyer type operators based on 2D-Appell polynomials. The investigation initiates by exploring the Korovkin-type approximation theorem and its convergence rates, employing both the traditional modulus of continuity and a class of Lipschitz functions. Following this, the study delves into the convergence of these operators within the weighted space of functions, providing estimates for their approximation properties. The establishment of a Voronovskaja-type asymptotic formula is also included. Furthermore, the article obtains statistical approximation properties for these operators through the application of a universal Korovkin-type statistical approximation theorem. The theoretical findings are reinforced by numerical and graphical examples, for different choice of parameters. |
| format | Article |
| id | doaj-art-e67c22b98bbc4b63a32e08fa2dead15e |
| institution | OA Journals |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-e67c22b98bbc4b63a32e08fa2dead15e2025-08-20T02:27:06ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-04-012025112610.1186/s13660-025-03300-yApproximation using Jakimovski–Leviatan operators of Durrmeyer type with 2D-Appell polynomialsManoj Kumar0Nusrat Raza1M. Mursaleen2Department of Mathematics, Aligarh Muslim UniversityMathematics section, Women’s College, Aligarh Muslim UniversityDepartment of Mathematical Sciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical SciencesAbstract This article delves into Jakimovski–Leviatan–Durrmeyer type operators based on 2D-Appell polynomials. The investigation initiates by exploring the Korovkin-type approximation theorem and its convergence rates, employing both the traditional modulus of continuity and a class of Lipschitz functions. Following this, the study delves into the convergence of these operators within the weighted space of functions, providing estimates for their approximation properties. The establishment of a Voronovskaja-type asymptotic formula is also included. Furthermore, the article obtains statistical approximation properties for these operators through the application of a universal Korovkin-type statistical approximation theorem. The theoretical findings are reinforced by numerical and graphical examples, for different choice of parameters.https://doi.org/10.1186/s13660-025-03300-y2D-Appell PolynomialsDurrmeyer operatorsJakimovski-Leviatan operatorsModulus of continuityStatistical approximation |
| spellingShingle | Manoj Kumar Nusrat Raza M. Mursaleen Approximation using Jakimovski–Leviatan operators of Durrmeyer type with 2D-Appell polynomials Journal of Inequalities and Applications 2D-Appell Polynomials Durrmeyer operators Jakimovski-Leviatan operators Modulus of continuity Statistical approximation |
| title | Approximation using Jakimovski–Leviatan operators of Durrmeyer type with 2D-Appell polynomials |
| title_full | Approximation using Jakimovski–Leviatan operators of Durrmeyer type with 2D-Appell polynomials |
| title_fullStr | Approximation using Jakimovski–Leviatan operators of Durrmeyer type with 2D-Appell polynomials |
| title_full_unstemmed | Approximation using Jakimovski–Leviatan operators of Durrmeyer type with 2D-Appell polynomials |
| title_short | Approximation using Jakimovski–Leviatan operators of Durrmeyer type with 2D-Appell polynomials |
| title_sort | approximation using jakimovski leviatan operators of durrmeyer type with 2d appell polynomials |
| topic | 2D-Appell Polynomials Durrmeyer operators Jakimovski-Leviatan operators Modulus of continuity Statistical approximation |
| url | https://doi.org/10.1186/s13660-025-03300-y |
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