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

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...

Full description

Saved in:
Bibliographic Details
Main Authors: S. V. R. Naidu, K. P. R. Rao, N. Srinivasa Rao
Format: Article
Language:English
Published: Wiley 2005-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/IJMMS.2005.1969
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850229353608118272
author S. V. R. Naidu
K. P. R. Rao
N. Srinivasa Rao
author_facet S. V. R. Naidu
K. P. R. Rao
N. Srinivasa Rao
author_sort S. V. R. Naidu
collection DOAJ
description 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.
format Article
id doaj-art-239bf4e89b0c4d3ca34566e5add1c601
institution OA Journals
issn 0161-1712
1687-0425
language English
publishDate 2005-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-239bf4e89b0c4d3ca34566e5add1c6012025-08-20T02:04:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005121969198810.1155/IJMMS.2005.1969On convergent sequences and fixed point theorems in D-metric spacesS. V. R. Naidu0K. P. R. Rao1N. Srinivasa Rao2Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, Andhra Pradesh 530 003, IndiaDepartment of Applied Mathematics, Acharya Nagarjuna University Post Graduate (ANUPG) Centre, Andhra Pradesh University, Nuzvid 521 201, IndiaDepartment of Applied Mathematics, Acharya Nagarjuna University Post Graduate (ANUPG) Centre, Andhra Pradesh University, Nuzvid 521 201, IndiaExamples 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.http://dx.doi.org/10.1155/IJMMS.2005.1969
spellingShingle S. V. R. Naidu
K. P. R. Rao
N. Srinivasa Rao
On convergent sequences and fixed point theorems in D-metric spaces
International Journal of Mathematics and Mathematical Sciences
title On convergent sequences and fixed point theorems in D-metric spaces
title_full On convergent sequences and fixed point theorems in D-metric spaces
title_fullStr On convergent sequences and fixed point theorems in D-metric spaces
title_full_unstemmed On convergent sequences and fixed point theorems in D-metric spaces
title_short On convergent sequences and fixed point theorems in D-metric spaces
title_sort on convergent sequences and fixed point theorems in d metric spaces
url http://dx.doi.org/10.1155/IJMMS.2005.1969
work_keys_str_mv AT svrnaidu onconvergentsequencesandfixedpointtheoremsindmetricspaces
AT kprrao onconvergentsequencesandfixedpointtheoremsindmetricspaces
AT nsrinivasarao onconvergentsequencesandfixedpointtheoremsindmetricspaces