  In this paper, we provide a unifying theory concerning the convergence
properties of the so-called max-product Kantorovich sampling operators based
upon generalized kernels in the setting of Orlicz spaces. The approximation of
functions defined on both bounded intervals and on the whole real axis has been
considered. Here, under suitable assumptions on the kernels, considered in
order to define the operators, we are able to establish a modular convergence
theorem for these sampling-type operators. As a direct consequence of the main
theorem of this paper, we obtain that the involved operators can be
successfully used for approximation processes in a wide variety of functional
spaces, including the well-known interpolation and exponential spaces. This
makes the Kantorovich variant of max-product sampling operators suitable for
reconstructing not necessarily continuous functions (signals) belonging to a
wide range of functional spaces. Finally, several examples of Orlicz spaces and
of kernels for which the above theory can be applied are presented.

Functional Analysis