Nonlinear multivariate sampling Durrmeyer operators: Convergence results and applications

In this paper, we introduce and study a class of nonlinear multivariate Durrmeyer sampling operators, extending to a multidimensional framework the univariate nonlinear operators previously investigated in [56]. Pointwise and uniform convergence results for bounded and, continuous or uniformly continuous functions, respectively, are established, ensuring a solid foundational understanding of the operators' approximation properties. Moving beyond classical settings, we extend our analysis to Orlicz spaces, which provide a suitable framework for handling signals that may not be continuous. Here, we prove a modular convergence theorem using a density argument. Additionally, examples of kernel functions are provided and graphical illustrations that visually demonstrate the convergence and reconstruction behavior of the operators are presented.