Approximation by means of nonlinear Kantorovich sampling type operators in Orlicz spaces

摘要

In this paper we introduce a nonlinear version of the Kantorovich sampling type series in a nonuniform setting. By means of the above series we are able to reconstruct signals (functions) which are continuous or uniformly continuous. Moreover, we study the problem of the convergence in the setting of Orlicz spaces: this allows us to treat signals which are not necessarily continuous. Our theory applies to L~p-spaces, interpolation spaces, exponential spaces and many others. Several graphical examples are provided.