P-cyclic c-contraction result in Menger spaces using a control function

• Autorzy: Choudhury B. S. , Bhandari S. K.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Menger space; Cauchy sequence; fixed point; Φ-function; C-contraction; Ψ-function

PL

przestrzeń Mengera; ciąg Cauchy'ego; punkt stały; φ-funkcja

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 2
• Strony: 213--223
• Opis fizyczny: Bibliogr. 37 poz.

Twórcy

autor

Choudhury B. S.

• Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur, Howrah-711103, India

autor

Bhandari S. K.

• Bhandari Department of Mathematics Bajkul Milani Mahavidyalaya P.O- Kismat Bajkul, Dist - Purba Medinipur Bajkul, West Bengal - 721655, India

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.