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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Bibliographic Details
Main Authors: Manoj Kumar, Nusrat Raza, M. Mursaleen
Format: Article
Language:English
Published: SpringerOpen 2025-04-01
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.
ISSN:1029-242X