Abstract

We give some theorems related to the contraction mapping principle of Banach-Caccioppoli and Edelstein. The contractive conditions we consider involve the quantities lim infξ→⋅d(ξ,fξ) and lim supξ→⋅d(ξ,fξ) instead of d(⋅,f⋅). Some examples are provided to show the difference between our results and the classical ones.