International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 15, Pages 2473-2489
Weak compatibility and fixed point theorems for four self-maps in -metric spaces
1School of Studies in Mathematics, Vikram University, University Road Ujjain, Madhya Pradesh 456010, India
2Mardi Bahuddin Khalsa College, Rajmohalla Indore, Madhya Pradesh, India
Received 21 September 2004; Revised 22 May 2005
Copyright © 2005 Bijendra Singh and Shobha Jain. 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.
This paper establishes one common coincident point theorem and three unique common fixed point theorems for four self-maps in -metric spaces, which improve and generalize, significantly, the results of Dhage et al. (2003), Dhage (1999), and Rhoades (2003) under weaker assumption using a more general contractive condition. An example, in support of these theorems, has also been constructed. All the results of this paper are new.