Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 614867, 13 pages
doi:10.1155/2010/614867
Research Article

Approximate Endpoints for Set-Valued Contractions in Metric Spaces

N. Hussain,1 A. Amini-Harandi,2 and Y. J. Cho3

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, University of Shahrekord Shahrekord, 88186-34141, Iran
3Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-70, Republic of Korea

Received 18 March 2010; Accepted 26 April 2010

Academic Editor: Mohamed Amine Khamsi

Copyright © 2010 N. Hussain et al. 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

The existence of approximate fixed points and approximate endpoints of the multivalued almost I-contractions is established. We also develop quantitative estimates of the sets of approximate fixed points and approximate endpoints for multivalued almost I-contractions. The proved results unify and improve recent results of Amini-Harandi (2010), M. Berinde and V. Berinde (2007), Ćirić (2009), M. Păcurar and R. V. Păcurar (2007) and many others.