International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1969-1988

On convergent sequences and fixed point theorems in D-metric spaces

S. V. R. Naidu,1 K. P. R. Rao,2 and N. Srinivasa Rao2

1Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, Andhra Pradesh 530 003, India
2Department of Applied Mathematics, Acharya Nagarjuna University Post Graduate (ANUPG) Centre, Andhra Pradesh University, Nuzvid 521 201, India

Received 24 March 2004; Revised 7 January 2005

Copyright © 2005 S. V. R. Naidu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Examples of complete D-metric spaces are given in which every convergent sequence has at most two limits and in which there are convergent sequences with exactly two limits. Also an example of a complete D-metric space having a convergent sequence with infinitely many limits is given and, using the example, several fixed point theorems in D-metric spaces are shown to be false. Modifications of some of these theorems and their generalizations are obtained either by imposing restrictions on the number of limits of certain convergent sequences in the space or by assuming the sequential continuity of the D-metric in any two variables and the theorems so obtained are illustrated by means of examples.