Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 412898, 12 pages
doi:10.1155/2009/412898
Research Article

Some New Weakly Contractive Type Multimaps and Fixed Point Results in Metric Spaces

Abdul Latif1 and Afrah A. N. Abdou2

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Science Faculty For Girls, King Abdulaziz University, P.O. Box 14884, Jeddah 21434, Saudi Arabia

Received 20 September 2009; Accepted 10 December 2009

Academic Editor: Marlene Frigon

Copyright © 2009 Abdul Latif and Afrah A. N. Abdou. 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

Some new weakly contractive type multimaps in the setting of metric spaces are introduced, and we prove some results on the existence of fixed points for such maps under certain conditions. Our results extend and improve several known results including the corresponding recent fixed point results of Pathak and Shahzad (2009), Latif and Abdou (2009), Latif and Albar (2008), Cirić (2008), Feng and Liu (2006), and Klim and Wardowski (2007).