On the completion of probabilistic metric spaces

1966 ◽  
Vol 6 (1) ◽  
pp. 62-64 ◽  
Author(s):  
H. Sherwood
Keyword(s):  
Metric Spaces ◽  
Probabilistic Metric Spaces ◽  
Probabilistic Metric

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.

Fixed point theorems in probabilistic metric spaces using property (E.A)

2013 ◽  
Vol 17 (2) ◽  
pp. 11-24
Author(s):  
Badridatt Pant ◽  
Brian Fisher ◽  
Sunny Chauhan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Probabilistic Metric Spaces ◽  
Probabilistic Metric
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