ON D-METRIC SPACES

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Published: May 1, 2014

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Ramabhadrasarma Ivatury
D. No.26-33-16/1, 7th Line, A.T.Agraharam, Guntur-522004, Andhra Pradesh, India.
sambasiva Rao siginam
SVS Group of Institutions, School of Engineering, Bheemaram, Warangal, Andhra Pradesh, India.

Abstract

The notion of a D-metric space was originally introduced by Dhage.  The concept of convergence of sequences in a D-metric space was introduced by him.  Some of his fixed point theorems were found to be incomplete or false by S.V.R. Naidu et al.  In this note we make use of a couple of important conditions mentioned by Dhage and obtain equivalence of D-metrics with appropriate metrics.  We also exhibit methods of generating D-metrics from certain types of real valued partial functions on the three dimensional Euclidean space.  We discuss various types of convergence in a D-metric space and verify implications and non-implications among them.

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How to Cite
Ivatury, R., & siginam, sambasiva R. (2014). ON D-METRIC SPACES. Journal of Global Research in Mathematical Archives(JGRMA), 1(12), 31–39. Retrieved from https://www.jgrma.com/index.php/jgrma/article/view/133
Issue
Vol. 1 No. 12 (2013): December-2013
Section
Research Paper

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Author Biographies

Ramabhadrasarma Ivatury, D. No.26-33-16/1, 7th Line, A.T.Agraharam, Guntur-522004, Andhra Pradesh, India.

Professor of Mathematics(Rtd),

Acharya Nagarjuna University,

Nagarjuna Nagar,

Guntur

sambasiva Rao siginam, SVS Group of Institutions, School of Engineering, Bheemaram, Warangal, Andhra Pradesh, India.

Assistant Professor,

Department of Humanities and Basic Sciences,

SVS Group of Institutions,

School of Engineering,

Warangal.

References

Dhage, B.C., (1994) : Generalized metric spaces and topological structure II, Pure .Appl. Math. Sci, 40 (1-2), 37-412.

Dhage , B.C., (2000) : Generalized metric spaces and topological structure I, Analene Stint, Univ. “A1.I, cuza “lasi 45, 3-24.

Naidu, S.V.R, Rao, K.P.R and Srinivasa Rao, N. (2004) : On the topology of D-metric spaces and the generation of D-metric spaces from metric spaces, Int.J.Math.Math.Sci 51, 2719-2740.