scholarly journals New Generalized Ekeland’s Variational Principle, Critical Point Theorems and Common Fuzzy Fixed Point Theorems Induced by Lin-Du’s Abstract Maximal Element Principle

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 11
Author(s):  
Junjian Zhao ◽  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Critical Point ◽  
Point Theorem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Ekeland’S Variational Principle ◽  
Ekeland's Variational Principle ◽  
Fuzzy Fixed Point ◽  
Element Theorem

In this paper, by applying the abstract maximal element principle of Lin and Du, we present some new existence theorems related with critical point theorem, maximal element theorem, generalized Ekeland’s variational principle and common (fuzzy) fixed point theorem for essential distances.

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.

On Equilibrium for Abstract Economies in GFC-Spaces

2014 ◽  
Vol 587-589 ◽  
pp. 2279-2284
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Kkm Mapping ◽  
Equilibrium Existence ◽  
Abstract Economies ◽  
Element Theorem ◽  
Qualitative Games

In this paper, the GFC-KKM mapping is introduced and GFC-KKM theorems are established in GFC-spaces. As applications, a fixed point theorem and maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, equilibrium existence theorems for qualitative games and abstract economies are yielded in GFC-spaces.

A fuzzy fixed-point theorem and its applications to maximal elements and Nash equilibria in noncompact CAT(0) spaces

2022 ◽  
pp. 1-18
Author(s):  
Haishu Lu ◽  
Rong Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Equilibrium Points ◽  
Maximal Elements ◽  
Nash Equilibrium Points ◽  
Fuzzy Fixed Point ◽  
Qualitative Games

In this paper, based on the KKM method, we prove a new fuzzy fixed-point theorem in noncompact CAT(0) spaces. As applications of this fixed-point theorem, we obtain some existence theorems of fuzzy maximal element points. Finally, we utilize these fuzzy maximal element theorems to establish some new existence theorems of Nash equilibrium points for generalized fuzzy noncooperative games and fuzzy noncooperative qualitative games in noncompact CAT(0) spaces. The results obtained in this paper generalize and extend many known results in the existing literature.

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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