scholarly journals Existence Theorems for Vector Equilibrium Problems via Quasi-Relative Interior

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Capătă Adela Elisabeta
Keyword(s):  
Equilibrium Problems ◽  
Existence Theorems ◽  
Relative Interior ◽  
Vector Equilibrium Problems ◽  
Quasi Relative Interior ◽  
Vector Equilibrium ◽  
Convexity Assumptions

The aim of this paper is to present new existence theorems for solutions of vector equilibrium problems, by using weak interior type conditions and weak convexity assumptions.

scholarly journals Existence and Duality of Generalized ε-Vector Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Hong-Yong Fu ◽  
Bin Dan ◽  
Xiang-Yu Liu
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Equilibrium Problem ◽  
Vector Equilibrium Problems ◽  
Kkm Theorem ◽  
Special Cases ◽  
Primal And Dual Problems ◽  
Primal And Dual ◽  
Vector Equilibrium

We consider a generalized ε-vector equilibrium problem which contain vector equilibrium problems and vector variational inequalities as special cases. By using the KKM theorem, we obtain some existence theorems for the generalized ε-vector equilibrium problem. We also investigate the duality of this generalized ε-vector equilibrium problem and discuss the equivalence relation between solutions of primal and dual problems.

scholarly journals Class𝔄-KKM(X,Y,Z), GeneralKKMType Theorems, and Their Applications in Topological Vector Space

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Gusheng Tang ◽  
Qingbang Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Vector Space ◽  
Topological Vector Space ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Equilibrium Problems ◽  
Matching Theorem ◽  
Generalized Vector Equilibrium Problems ◽  
Vector Equilibrium

The class𝔄-KKM(X,Y,Z)and generalizedKKMmapping are introduced, and some generalizedKKMtheorems are proved. As applications, Ky Fan’s matching theorem and Fan-Browder fixed-point theorem are extended, and some existence theorems of solutions for the generalized vector equilibrium problems are established under noncompact setting, which improve and generalize some known results.

scholarly journals Implicit vector equilibrium problems via nonlinear scalarisation

2005 ◽  
Vol 72 (1) ◽  
pp. 161-172 ◽  
Author(s):  
Jun Li ◽  
Nan-Jing Huang
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Equilibrium Problem ◽  
Vector Equilibrium Problems ◽  
Vector Equilibrium

The purpose of this paper is to introduce a nonlinear scalarisation function for solving a class of implicit vector equilibrium problems. We prove a scalarisation lemma to show the relation between the implicit vector equilibrium problem and the nonlinear scalarisation function. Then we derive some new existence theorems for solutions of implicit vector equilibrium problems, using the scalarisation lemma and the FKKM theorem.

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