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

• Main Authors: Choudhury B. S., Bhandari S. K.
• Format: Article
• Language: English
• Published: De Gruyter 2016-06-01
• Series: Demonstratio Mathematica
• Subjects: Menger space; Cauchy sequence; fixed point; Φ-function; C-contraction; Ψ-function
• Online Access: http://www.degruyter.com/view/j/dema.2016.49.issue-2/dema-2016-0018/dema-2016-0018.xml?format=INT

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.