Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 510974, 12 pages
doi:10.1155/2010/510974
Research Article

Fixed Point and Best Proximity Theorems under Two Classes of Integral-Type Contractive Conditions in Uniform Metric Spaces

M. De la Sen

Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia), P.O. Box. 644- Bilbao, 48080 Bilbao, Spain

Received 5 July 2010; Accepted 14 October 2010

Academic Editor: S. Reich

Copyright © 2010 M. De la Sen. 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

This paper investigates the existence of fixed points and best proximity points of p-cyclic self-maps on a set of subsets of a certain uniform space under integral-type contractive conditions. The parallel properties of the associated restricted composed maps from any of the subsets to itself are also investigated. The subsets of the uniform space are not assumed to intersect.