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International Journal of Analysis
Volume 2013 (2013), Article ID 763261, 10 pages
http://dx.doi.org/10.1155/2013/763261
Research Article

Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems

1Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
2Near Nehru Training Centre, H. No. 274, Nai Basti B-14, Bijnor, Uttar Pradesh 246 701, India

Received 29 January 2013; Accepted 4 April 2013

Academic Editor: Chuanxi Qian

Copyright © 2013 Mohammad Imdad and Sunny Chauhan. 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 purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in metric spaces satisfying an implicit function essentially due to the paper of Ali and Imdad (2008). As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Ali and Imdad (2008). We also furnish some illustrative examples to support our main results.