Fixed Point Theorems for Contractive Mappings in Complete G-Metric Spaces

Metric spaces are playing an increasing role in mathematics and the applied sciences. Over the past two decades the development of fixed point theory in metric spaces has attracted considerable attention due to numerous applications in areas such as variational and linear inequalities, optimization, and approximation theory. Different generalizations of the notion of a metric space have been proposed by Gahler 1, 2 and by Dhage 3, 4 . However, HA et al. 5 have pointed out that the results obtained by Gahler for his 2 metrics are independent, rather than generalizations, of the corresponding results in metric spaces, while in 6 the current authors have pointed out that Dhage’s notion of a D-metric space is fundamentally flawed and most of the results claimed by Dhage and others are invalid. In 2003 we introduced a more appropriate and robust notion of a generalized metric space as follows.