Ekeland's variational principle and Caristi's fixed point theorem in probabilistic metric space

1991 ◽  
Vol 7 (3) ◽  
pp. 217-228 ◽  
Author(s):  
Shisheng Zhang ◽  
Yuqing Chen ◽  
Jinli Guo
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Ekeland’S Variational Principle ◽  
Probabilistic Metric Space ◽  
Ekeland's Variational Principle ◽  
Caristi’S Fixed Point Theorem ◽  
Probabilistic Metric

scholarly journals A generalized form of Ekeland’s variational principle

2012 ◽  
Vol 20 (1) ◽  
pp. 101-112 ◽  
Author(s):  
Csaba Farkas
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Ekeland’S Variational Principle ◽  
Ekeland Variational Principle ◽  
Ekeland's Variational Principle ◽  
Common Generalization

Abstract In this paper we prove a generalized version of the Ekeland variational principle, which is a common generalization of Zhong variational principle and Borwein Preiss Variational principle. Therefore in a particular case, from this variational principle we get a Zhong type variational principle, and a Borwein-Preiss variational principle. As a consequence, we obtain a Caristi type fixed point theorem.

scholarly journals Generalized Ekeland’s variational principle with applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Eshagh Hashemi ◽  
Reza Saadati ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Fixed Point Theorem ◽  
Equilibrium Problem ◽  
Point Theorem ◽  
Ekeland’S Variational Principle ◽  
Ekeland's Variational Principle ◽  
Nadler’S Fixed Point Theorem

Abstract By using the concept of Γ-distance, we prove EVP (Ekeland’s variational principle) on quasi-F-metric (q-F-m) spaces. We apply EVP to get the existence of the solution to EP (equilibrium problem) in complete q-F-m spaces with Γ-distances. Also, we generalize Nadler’s fixed point theorem.

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