Coupled fixed point results in generalized metric spaces

The study of fixed points of mappings satisfying certain contractive conditions has been at the center of rigorous research activity, see 1–3 . The notion ofD-metric space is a generalization of usual metric spaces and it is introduced by Dhage 4–7 . Recently, Mustafa and Sims 8, 9 have shown that most of the results concerning Dhage’sD-metric spaces are invalid. In 8, 9 , they introduced an improved version of the generalized metric space structure which they called G-metric spaces. For more results on G-metric spaces, one can refer to the papers 10– 26 . Now, we give some preliminaries and basic definitions which are used throughout the paper. In 2006, Mustafa and Sims 9 introduced the concept of G-metric spaces as follows.