Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 197308, 9 pages
doi:10.1155/2009/197308
Research Article

Best Proximity Point Theorems for p-Cyclic Meir-Keeler Contractions

S. Karpagam and Sushama Agrawal

Department of Mathematics, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai 600 005, India

Received 31 August 2008; Revised 21 November 2008; Accepted 5 January 2009

Academic Editor: Tomonari Suzuki

Copyright © 2009 S. Karpagam and Sushama Agrawal. 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 consider a contraction map T of the Meir-Keeler type on the union of p subsets A1,…,Ap, (p≥2), of a metric space (X,d) to itself. We give sufficient conditions for the existence and convergence of a best proximity point for such a map.