International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 786814, 12 pages
Research Article

Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings

Department of Mathematics, Kumaun University, D. S. B. Campus, Nainital 263002, India

Received 20 March 2012; Revised 19 May 2012; Accepted 2 June 2012

Academic Editor: Naseer Shahzad

Copyright © 2012 R. K. Bisht. 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.


The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of weak reciprocal continuity. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. We demonstrate that weak reciprocal continuity ensures the existence of common fixed points under contractive conditions, which otherwise do not ensure the existence of fixed points. Our results generalize and extend Banach contraction principle and Meir-Keeler-type fixed point theorem.