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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |