Table of Contents
Journal of Operators
Volume 2013, Article ID 186910, 11 pages
Research Article

Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation

1Department of Mathematics, R.H. Government Postgraduate College, Kashipur 244 713, U.S. Nagar, Uttarakhand, India
2Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
3Università degli Studi di Palermo, Dipartimento di Matematica e Informatica, Via Archirafi 34, 90123 Palermo, Italy

Received 29 March 2013; Accepted 22 May 2013

Academic Editor: Lingju Kong

Copyright © 2013 Sunny Chauhan 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 prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized 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. Moreover, we study the existence of solutions of a nonlinear integral equation.