Approximation using Jakimovski–Leviatan operators of Durrmeyer type with 2D-Appell polynomials

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.