Unique fixed points of p-cyclic kannan type probabilistic contractions

Choudhury, Binayak S.; Bhandari, Samir Kumar; Saha, P.

doi:10.1007/s40574-016-0073-1

Cited by 3 publications

(1 citation statement)

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“…Some fixed point results of p-cyclic maps have been obtained in [9,20,21,34]. In this paper, we are interested in the fixed point properties of p-cyclic mappings of C-contraction in probabilistic metric spaces.…”

Section: Introductionmentioning

confidence: 99%

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

Choudhury

Bhandari²

2016

Demonstratio Mathematica

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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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Section: Introductionmentioning

confidence: 99%

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

Choudhury

Bhandari²

2016

Demonstratio Mathematica

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Probabilistic p-cyclic contractions using different types of t-norms

Choudhury

Bhandari²,

Saha

2018

Random Operators and Stochastic Equations

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Cyclic mappings have appeared prominently in fixed point theory during the last decade. They have also their applications in global optimization problems. Note that p-cyclic mappings are extensions of cyclic mappings over p number of sets. In this paper we introduce two p-cyclic contractions in probabilistic spaces. We have two corresponding fixed point theorems using third-order Hadzic-type t-norm and minimum t-norm, respectively. One of the probabilistic contractions is of Ciric type while the other is a general contraction. One illustrative example is given. The space we consider here is a 2-Menger space which is an extension of a probabilistic metric space in the same vein as the 2-metric spaces are extensions of metric spaces.

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