Caristi type hybrid fixed point theorems in menger probabilistic metric space

1997 ◽  
Vol 18 (2) ◽  
pp. 201-209 ◽  
Author(s):  
Shi Chuan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric ◽  
Menger Probabilistic Metric Space

scholarly journals On a probabilistic version of Meir-Keeler type fixed point theorem for a family of discontinuous operators

2021 ◽  
Vol 22 (2) ◽  
pp. 435
Author(s):  
Ravindra K. Bisht ◽  
Vladimir Rakocević
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Point Property ◽  
Probabilistic Metric Space ◽  
Discontinuous Mappings ◽  
Probabilistic Metric ◽  
Menger Probabilistic Metric Space ◽  
Probabilistic Version

<p>A Meir-Keeler type fixed point theorem for a family of mappings is proved in Menger probabilistic metric space (Menger PM-space). We establish that completeness of the space is equivalent to fixed point property for a larger class of mappings that includes continuous as well as discontinuous mappings. In addition to it, a probabilistic fixed point theorem satisfying (ϵ - δ) type non-expansive mappings is established.</p>

scholarly journals Common Fixed Points for JH-Operators and Occasionally Weakly g-Biased Pairs under Relaxed Condition on Probabilistic Metric Space

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Arvind Bhatt ◽  
Harish Chandra
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Triangle Inequality ◽  
Common Fixed Points ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric

We obtain some fixed point theorems for JH-operators and occasionally weakly g-biased maps on a setXtogether with the functionF:X×X→Δwithout using the triangle inequality and without using the symmetric condition. Our results extend the results of Bhatt et al. (2010).

scholarly journals Multivalued operator with respect generalized distance on Menger probabilistic metric spaces

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1675-1682
Author(s):  
Reza Saadati
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Multivalued Operator ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric Spaces ◽  
Contractive Type ◽  
Probabilistic Metric ◽  
Menger Probabilistic Metric Space ◽  
Generalized Distance

In this paper, we recall the concept of r-distance on a Menger probabilistic metric space. Further we prove a fixed point theorem for contractive type multi-valued operators in terms of a r-distance on a complete Menger probabilistic metric space.

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.

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