Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 509658, 8 pages
doi:10.1155/2010/509658
Research Article

A Common End Point Theorem for Set-Valued Generalized ( 𝜓 , 𝜙 ) -Weak Contraction

Mujahid Abbas1 and Dragan Ðorić2

1Department of Mathematics, Centre for Advanced Studies in Mathematics, Lahore University of Management Sciences, 54792 Lahore, Pakistan
2Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, 11000 Beograd, Serbia

Received 21 August 2010; Accepted 18 October 2010

Academic Editor: Satit Saejung

Copyright © 2010 Mujahid Abbas and Dragan Ðorić. 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 introduce the class of generalized ( 𝜓 , 𝜙 ) -weak contractive set-valued mappings on a metric space. We establish that such mappings have a unique common end point under certain weak conditions. The theorem obtained generalizes several recent results on single-valued as well as certain set-valued mappings.