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

Liminf and limsup contractions

Viale Martiri della Libertà n. 20, Macerata 62100, Italy

Received 15 March 2001

Copyright © 2001 Hindawi Publishing Corporation. 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 infξd(ξ,fξ) and lim supξd(ξ,fξ) instead of d(,f). Some examples are provided to show the difference between our results and the classical ones.