The multivariate Durrmeyer-sampling type operators: approximation in Orlicz spaces

This paper deals with the study of the convergence of the family of multivariate Durrmeyer-sampling type operators in the general setting of Orlicz spaces. The above result implies also the convergence in remarkable subcases, such as in Lebesgue, Zygmund and exponential spaces. Convergence results have been established also in case of continuous functions, where pointwise and uniform convergence theorems, including some quantitative estimates, have been achieved. Finally, several examples with graphical representations are given.