ON D-METRIC SPACES - Ivatury, Ramabhadrasarma; siginam, sambasiva Rao (Journal of Global Research in Mathematical Archives(JGRMA), 2014)
The notion of a D-metric space was originally introduced by Dhage.Â The concept of convergence of sequences in a D-metric space was introduced by him.Â Some of his fixed point theorems were found to be incomplete or false by S.V.R. Naidu et al.Â In this note we make use of a couple of important conditions mentioned by Dhage and obtain equivalence of D-metrics with appropriate metrics.Â We also exhibit methods of generating D-metrics from certain types of real valued partial functions on the three dimensional Euclidean space.Â We discuss various types of convergence in a D-metric space and verify implications and non-implications among them.