Systems of equilibrium problems with applications to new variants of Ekeland’s variational principle, fixed point theorems and parametric optimization problems

2007 ◽  
Vol 40 (4) ◽  
pp. 663-677 ◽  
Author(s):  
Lai-Jiu Lin ◽  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Fixed Point Theorems ◽  
Parametric Optimization ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Ekeland’S Variational Principle ◽  
Ekeland's Variational Principle

scholarly journals Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Equilibrium Problem ◽  
Optimization Problems ◽  
Existence Theorems ◽  
Ekeland’S Variational Principle ◽  
Equivalence Relations ◽  
Quasi Equilibrium ◽  
Ekeland's Variational Principle ◽  
Topological Vector Spaces

By applying hybrid inclusion and disclusion systems (HIDS), we establish several vectorial variants of system of Ekeland's variational principle on topological vector spaces, some existence theorems of system of parametric vectorial quasi-equilibrium problem, and an existence theorem of system of the Stampacchia-type vectorial equilibrium problem. As an application, a vectorial minimization theorem is also given. Moreover, we discuss some equivalence relations between our vectorial variant of Ekeland's variational principle, common fixed point theorem, and maximal element theorem.

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.

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