Convergence of sampling Kantorovich operators in modular spaces with applications

In the present paper we study the so-called sampling Kantorovich operators in the very general setting of modular spaces. Here, modular convergence theorems are proved under suitable assumptions, together with a modular inequality for the above operators. Further, we study applications of such approximation results in several concrete cases, such as Musielak–Orlicz and Orlicz spaces. As a consequence of these results we obtain convergence theorems in the classical and weighted versions of the Lp and Zygmund (or interpolation) spaces. At the end of the paper examples of kernels for the above operators are presented.