A general method to study the convergence of nonlinear operators in Orlicz spaces

Abstract

Abstract We continue the work started in a previous article and introduce a general setting in which we define nets of nonlinear operators whose domains are some set of functions defined in a locally compact topological group. We analyze the behavior of such nets and detect the fairest assumption, which are needed for the nets to converge with respect to the uniform convergence and in the setting of Orlicz spaces. As a consequence, we give results of convergence in this frame, study some important special cases, and provide graphical representations.