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Abstract and Applied Analysis
Volume 2013, Article ID 313782, 6 pages
Research Article

On Fixed Points of -Contractive Multivalued Mappings in Cone Metric Spaces

1Department of Mathematics, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, COMSATS Institute of Information Technology, Chak Shahzad, Islamabad 44000, Pakistan

Received 10 July 2013; Revised 13 September 2013; Accepted 19 September 2013

Academic Editor: Salvador Romaguera

Copyright © 2013 Marwan Amin Kutbi 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.


We define the notion of -contractive mappings for cone metric space and obtain fixed points of multivalued mappings in connection with Hausdorff distance function for closed bounded subsets of cone metric spaces. We obtain some recent results of the literature as corollaries of our main theorem. Moreover, a nontrivial example of -contractive mapping satisfying all conditions of our main result has been constructed.