Generic contractivity for a class of nonlinear mappings

Abstract

In a previous paper of ours we studied a class of nonlinear self-mappings of a complete metric space endowed with a natural metric. Using the notion of porosity, we showed that most elements of this class possess a unique fixed point which attracts all iterates uniformly. In the present paper we prove a variant of this result by showing that most mappings in this class are quasi-contractive