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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-04-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-025-03300-y |
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| Summary: | 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. |
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| ISSN: | 1029-242X |