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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1969 |
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| _version_ | 1850229353608118272 |
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| 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 |