Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 390183, 7 pages
doi:10.1155/2010/390183
Research Article

Fixed Point Theorems for Set-Valued Contraction Type Maps in Metric Spaces

A. Amini-Harandi1 and D. O'Regan2

1Department of Mathematics, University of Shahrekord, Shahrekord, 88186-34141, Iran
2Department of Mathematics, National University of Ireland, Galway, Ireland

Received 13 August 2009; Revised 15 October 2009; Accepted 13 January 2010

Academic Editor: Mohamed A. Khamsi

Copyright © 2010 A. Amini-Harandi and D. O'Regan. 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 first give some fixed point results for set-valued self-map contractions in complete metric spaces. Then we derive a fixed point theorem for nonself set-valued contractions which are metrically inward. Our results generalize many well-known results in the literature.