Fixed points of contraction mappings on probabilistic metric spaces

1972 ◽  
Vol 6 (1-2) ◽  
pp. 97-102 ◽  
Author(s):  
V. M. Sehgal ◽  
A. T. Bharucha-Reid
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Probabilistic Metric Spaces ◽  
Contraction Mappings ◽  
Probabilistic Metric

scholarly journals Some Fixed Point Theorems in Generalized Probabilistic Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chuanxi Zhu ◽  
Wenqing Xu ◽  
Zhaoqi Wu
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Probabilistic Metric Spaces ◽  
Contraction Mappings ◽  
Probabilistic Metric

We introduce the concepts of(H,ψ,Φ)-contraction and probabilistic(α,φ)-contraction mappings in generalized probabilistic metric spaces and prove some fixed point theorems for such two types of mappings in generalized probabilistic metric spaces. Our results generalize and extend many comparable results in existing literature. Some examples are also given to support our results. Finally, an application to the existence of solutions for a class of integral equations is presented by utilizing one of our main results.

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 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 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.

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