On compactness of probabilistic metric space

2014 ◽  
Vol 8 ◽  
pp. 1703-1710
Author(s):  
Abderrahim Mbarki ◽  
Abedelmalek Ouahab ◽  
Naciri Rachid
Keyword(s):  
Metric Space ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric

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 Generalized contraction mapping in probabilistic metric space

1970 ◽  
Vol 7 (1) ◽  
pp. 79-91
Author(s):  
Shams-ur Rahman ◽  
K Jha
Keyword(s):  
Fixed Point ◽  
Distribution Function ◽  
Metric Space ◽  
Contraction Mapping ◽  
Probabilistic Metric Space ◽  
Generalized Contraction ◽  
Point Distribution ◽  
Contraction Mappings ◽  
Historical Developments ◽  
Probabilistic Metric

The probabilistic metric space as one of the important generalization of metric space was introduced by K. Menger in 1942. In this paper, we briefly discuss the historical developments of contraction mappings in probabilistic metric space with some fixed point results. Keywords: Fixed point; Distribution function; t-norm; PM space; contraction mapping. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5425 KUSET 2011; 7(1): 79-91

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