\(\sigma \)-porous sets of generalised nonexpansive mappings (Q2925777)

Various authors have studied problems of the following form. Let \(S\) be the space of all maps which satisfy some conditions of nonexpansive type; how big is the set of maps of \(S\) which have some given fixed point properties (e.g., existence, uniqueness, convergence of the iterates, etc.) with respect to \(S\)? In general, the answer is that the set of these maps is big; indeed, its complement in \(S\) is of the first category or even \(\sigma\)-lower porous. In this paper, the author states a general theorem which contains and extends some previous results of other authors. He also applies the theorem to the study of the existence of attractors of nonexpansive iterated function systems.