Vector Equilibrium Problems. Existence Theorems and Convexity of Solution Set

2005 ◽  
Vol 31 (1) ◽  
pp. 109-119 ◽  
Author(s):  
Jun-Yi Fu
2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Hong-Yong Fu ◽  
Bin Dan ◽  
Xiang-Yu Liu

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.


2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Capătă Adela Elisabeta

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Gusheng Tang ◽  
Qingbang Zhang

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.


Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2097-2105 ◽  
Author(s):  
A.P. Farajzadeh

In this paper, without assumption of monotonicity and boundedness, we study existence results for a solution and the convexity of the solution set to the symmetric vector equilibrium problem for setvalued mappings in the setting of topological vector spaces. Our results improve the corresponding results in [9, 18, 19, 22, 28, 33, 36, 37].


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