Fixed and periodic points of local contraction mappings on probabilistic metric spaces

1975 ◽  
Vol 9 (3) ◽  
pp. 289-297 ◽  
Author(s):  
G. L. Cain ◽  
R. H. Kasriel
Keyword(s):  
Metric Spaces ◽  
Periodic Points ◽  
Probabilistic Metric Spaces ◽  
Contraction Mappings ◽  
Local Contraction ◽  
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 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.

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