P-Cyclic C-Contraction Result in Menger Spaces Using a Control Function
The intrinsic flexibility of probabilistic metric spaces makes it possible to extend the idea of contraction mapping in several inequivalent ways, one of which being the C-contraction. Cyclic contractions are another type of contractions used extensively in global optimization problems. We introduce...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2016-06-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/dema.2016.49.issue-2/dema-2016-0018/dema-2016-0018.xml?format=INT |
| Summary: | The intrinsic flexibility of probabilistic metric spaces makes it possible to extend the idea of contraction mapping in several inequivalent ways, one of which being the C-contraction. Cyclic contractions are another type of contractions used extensively in global optimization problems. We introduced here p-cyclic contractions which are probabilistic C-contraction types. It involves p numbers of subsets of the spaces and involves two control functions for its definitions. We show that such contractions have fixed points in a complete probabilistic metric space. The main result is supported with an example and extends several existing results. |
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| ISSN: | 0420-1213 2391-4661 |