International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 5, Pages 789-801
doi:10.1155/IJMMS.2005.789

Semicompatibility and fixed point theorems in an unbounded D-metric space

Bijendra Singh1 , Shishir Jain2 and Shobha Jain3

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

Abstract

Rhoades (1996) proved a fixed point theorem in a bounded D-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unbounded D-metric space, for two self-maps satisfying a general contractive condition with a restricted domain of x and y. This has been done by using the notion of semicompatible maps in D-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 D-metric spaces. All the results of this paper are new.