Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 708984, 13 pages
doi:10.1155/2010/708984
Research Article

Common Fixed Point of Multivalued Generalized φ-Weak Contractive Mappings

Behzad Djafari Rouhani1 and Sirous Moradi2

1Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA
2Department of Mathematics, Faculty of Science, University of Arak, Arak 38156-879, Iran

Received 18 September 2009; Accepted 10 January 2010

Academic Editor: Mohamed A. Khamsi

Copyright © 2010 Behzad Djafari Rouhani and Sirous Moradi. 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

Fixed point and coincidence results are presented for multivalued generalized φ-weak contractive mappings on complete metric spaces, where φ:[0,+∞)→[0,+∞) is a lower semicontinuous function with φ(0)=0 and φ(t)>0 for all t>0. Our results extend previous results by Zhang and Song (2009), as well as by Rhoades (2001), Nadler (1969), and Daffer and Kaneko (1995).