scholarly journals Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Manuel De la Sen ◽  
Erdal Karapınar
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Convex Banach Space ◽  
Probabilistic Metric Spaces ◽  
Best Proximity Points ◽  
Menger Spaces ◽  
Cyclic Contractions ◽  
Probabilistic Metric

This paper investigates properties of convergence of distances ofp-cyclic contractions on the union of thepsubsets of an abstract setXdefining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points ofp-cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of thep-composite mappings restricted to each of thepsubsets in the cyclic disposal are also investigated and some illustrative examples are given.

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

2016 ◽  
Vol 49 (2) ◽  
Author(s):  
B. S. Choudhury ◽  
S. K. Bhandari
Keyword(s):  
Contraction Mapping ◽  
Metric Spaces ◽  
Optimization Problems ◽  
Control Function ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric Spaces ◽  
Control Functions ◽  
Menger Spaces ◽  
Cyclic Contractions ◽  
Probabilistic Metric

AbstractThe 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.

scholarly journals On Probabilistic Alpha-Fuzzy Fixed Points and Related Convergence Results in Probabilistic Metric and Menger Spaces under Some Pompeiu-Hausdorff-Like Probabilistic Contractive Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Probabilistic Metric Spaces ◽  
Convergence Results ◽  
Menger Spaces ◽  
Convergence Of Sequences ◽  
Probabilistic Metric

In the framework of complete probabilistic metric spaces and, in particular, in probabilistic Menger spaces, this paper investigates some relevant properties of convergence of sequences to probabilisticα-fuzzy fixed points under some types of probabilistic contractive conditions.

scholarly journals Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces

2019 ◽  
Vol 24 (5) ◽  
Author(s):  
Shahnaz Jafari ◽  
Maryam Shams ◽  
Asier Ibeas ◽  
Manuel De La Sen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Linear Combination ◽  
Metric Space ◽  
Metric Spaces ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric Spaces ◽  
Contractive Mappings ◽  
Probabilistic Metric ◽  
Infinite Linear

In this paper, we introduce the concept of enhanced probabilistic metric space (briefly EPM-space) as a type of probabilistic metric space. Also, we investigate the existence of fixed points for a (finite or infinite) linear combination of different types of contractive mappings in EPM-spaces. Furthermore, we investigate about the convergence of sequences (generated by a finite or infinite family of contractive mappings) to a common fixed point. The useful application of this research is the study of the stability of switched dynamic systems, where we study the conditions under which the iterative sequences generated by a (finite or infinite) linear combination of mappings (contractive or not), converge to the fixed point. Also, some examples are given to support the obtained results. In the end, a number of figures give us an overview of the examples.

scholarly journals Altering distances and a common fixed point theorem in Menger probabilistic metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 175-181
Author(s):  
Sinisa Jesic ◽  
Natasa Cirovic ◽  
Donal O’Regan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Probabilistic Metric Spaces ◽  
Menger Spaces ◽  
Contractive Type ◽  
Probabilistic Metric ◽  
Common Fixed Point Theorem

This paper presents a common fixed point theorem for two compatible self-mappings satisfying nonlinear contractive type condition defined using a ?-function. This result extends previous results due to B. S. Choudhury, K. Das, A new contraction principle in Menger spaces, Acta Mathematica Sinica 24 (2008) 1379-1386, and the result due to D. Mihe?, Altering distances in probabilistic Menger spaces, Nonlinear Analysis 71 (2009) 2734-2738.

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