International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 7, Pages 395-402
doi:10.1155/S0161171201007086

liminf and limsup contractions

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.