New existence theorems for quasi-equilibrium problems and a minimax theorem on complete metric spaces

2012 ◽  
Vol 57 (2) ◽  
pp. 533-547 ◽  
Author(s):  
Chih-Sheng Chuang ◽  
Lai-Jiu Lin
Keyword(s):  
Metric Spaces ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Minimax Theorem ◽  
Quasi Equilibrium ◽  
Complete Metric Spaces

scholarly journals System of Operator Quasi Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Suhel Ahmad Khan
Keyword(s):  
Maximal Element ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Quasi Equilibrium ◽  
Basic Tool ◽  
Maximal Element Theorem ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Element Theorem

We consider a system of operator quasi equilibrium problems and system of generalized quasi operator equilibrium problems in topological vector spaces. Using a maximal element theorem for a family of set-valued mappings as basic tool, we derive some existence theorems for solutions to these problems with and without involving Φ-condensing mappings.

scholarly journals Ekeland-type variational principle with applications to nonconvex minimization and equilibrium problems

2019 ◽  
Vol 24 (3) ◽  
pp. 407-432
Author(s):  
Iram Iqbal ◽  
Nawab Hussain
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Metric Spaces ◽  
Equilibrium Problems ◽  
Lower Semicontinuous ◽  
Minimax Theorem ◽  
Nonconvex Minimization ◽  
Equilibrium Theorem

The aim of the present paper is to establish a variational principle in metric spaces without assumption of completeness when the involved function is not lower semicontinuous. As consequences, we derive many fixed point results, nonconvex minimization theorem, a nonconvex minimax theorem, a nonconvex equilibrium theorem in noncomplete metric spaces. Examples are also given to illustrate and to show that obtained results are proper generalizations.

scholarly journals Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1604
Author(s):  
Jing-Nan Li ◽  
San-Hua Wang ◽  
Yu-Ping Xu
Keyword(s):  
Equilibrium Problems ◽  
Existence Theorems ◽  
Saddle Points ◽  
Upper Semicontinuity ◽  
Quasi Equilibrium ◽  
Solution Sets ◽  
Variable Ordering ◽  
Variable Ordering Structures ◽  
The One ◽  
Cone Convexity

In this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed. By using the concept of cosmically upper continuity rather than the one of upper semicontinuity for cone-valued mapping, some existence theorems of solutions are established under suitable assumptions of cone-continuity and cone-convexity for the equilibrium mappings. Moreover, the results of compactness for solution sets are proven. As applications, some existence results of strong saddle points are obtained. The main results obtained in this paper unify and improve some recent works in the literature.

scholarly journals Vector quasi-equilibrium problems

2003 ◽  
Vol 68 (2) ◽  
pp. 295-302 ◽  
Author(s):  
Abdul Khaliq ◽  
Sonam Krishan
Keyword(s):  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Quasi Equilibrium ◽  
Topological Vector Spaces

In this paper we establish existence theorems for vector quasi-equilibrium problems in Hausdorff topological vector spaces both under compactness and noncompactness assumptions.

scholarly journals Existence of solutions for a system of quasi-variational relation problems and some applications

2015 ◽  
Vol 31 (1) ◽  
pp. 135-142
Author(s):  
ZHE YANG ◽  
Keyword(s):  
Nash Equilibrium ◽  
Maximal Element ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Quasi Equilibrium ◽  
Variational Inclusions ◽  
New Class

In this paper, we study the existence of solutions for a new class of systems of quasi-variational relation problems on different domains. As applications, we obtain existence theorems of solutions for systems of quasi-variational inclusions, systems of quasi-equilibrium problems, systems of generalized maximal element problems, systems of generalized KKM problems and systems of generalized quasi-Nash equilibrium problems on different domains. The results of this paper improve and generalize several known results on variational relation problems.

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