International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 7, Pages 395-402
doi:10.1155/S0161171201007086
Liminf and limsup contractions
Viale Martiri della Libertà n. 20, Macerata 62100, Italy
Received 15 March 2001
Copyright © 2001 Alberto Branciari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.