International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 5, Pages 789-801
Semicompatibility and fixed point theorems in an unbounded -metric space
1School of Studies in Mathematics, Vikram University, Ujjain 456010, Madhya Pradesh, India
2Shri Vaishnav Institute of Technology & Science, Gram Baroli, Alwasa, Indore 453331, Madhya Pradesh, India
3MB Khalsa College, Raj Mohalla, Indore 452002, Madhya Pradesh, India
Received 16 March 2004; Revised 24 August 2004
Copyright © 2005 Bijendra Singh 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.
Rhoades (1996) proved a fixed point theorem in a bounded -metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unbounded -metric space, for two self-maps satisfying a general contractive condition with a restricted domain of and . This has been done by using the notion of semicompatible maps in -metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory of -metric spaces. All the results of this paper are new.