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P-Cyclic C-Contraction Result in Menger Spaces Using a Control Function

P-Cyclic C-Contraction Result in Menger Spaces Using a Control Function Abstract 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

P-Cyclic C-Contraction Result in Menger Spaces Using a Control Function

Demonstratio Mathematica , Volume 49 (2) – Jun 1, 2016

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
2391-4661
eISSN
0420-1213
DOI
10.1515/dema-2016-0018
Publisher site
See Article on Publisher Site

Abstract

Abstract 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.

Journal

Demonstratio Mathematicade Gruyter

Published: Jun 1, 2016

References