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

B. S. Choudhury 1  and S. K. Bhandari 2
  • 1 DEPARTMENT OF MATHEMATICS INDIAN INSTITUTE OF ENGINEERING SCIENCE AND TECHNOLOGY SHIBPUR, HOWRAH-711103, INDIA
  • 2 DEPARTMENT OF MATHEMATICS BAJKUL MILANI MAHAVIDYALAYA P.O- KISMAT BAJKUL, DIST - PURBA MEDINIPUR BAJKUL, WEST BENGAL - 721655, INDIA

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.

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