scholarly journals Feasibility-solvbility theorems for generalized vector equilibrium problem in reflexive banach spaces

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Gang Wang ◽  
Hai-tao Che ◽  
Hai-bin Chen
Keyword(s):  
Equilibrium Problem ◽  
Banach Spaces ◽  
Vector Equilibrium Problem ◽  
Reflexive Banach Spaces ◽  
Generalized Vector Equilibrium Problem ◽  
Vector Equilibrium

Connectedness of the sets of weak efficient solutions for generalized vector equilibrium problems

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Qing-You Liu ◽  
Xian-Jun Long ◽  
Nan-jing Huang
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Efficient Solutions ◽  
Vector Equilibrium Problem ◽  
Vector Equilibrium Problems ◽  
Generalized Vector Equilibrium Problem ◽  
Generalized Vector Equilibrium Problems ◽  
Vector Equilibrium ◽  
Locally Convex

AbstractIn this paper, a generalized vector equilibrium problem is introduced and studied. A scalar characterization of weak efficient solutions for the generalized vector equilibrium problem is obtained. By using the scalarization result, the existence of the weak efficient solutions and the connectedness of the set of weak efficient solutions for the generalized vector equilibrium problem are proved in locally convex spaces.

scholarly journals Generalized strongly vector equilibrium problem for set-valued mappings

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1783-1790 ◽  
Author(s):  
Rais Ahmad ◽  
Mijanur Rahaman
Keyword(s):  
Equilibrium Problem ◽  
Banach Spaces ◽  
Existence Theorems ◽  
Vector Equilibrium Problem ◽  
Fan Theorem ◽  
Set Valued Mappings ◽  
Vector Equilibrium

In this paper, we introduce and study a generalized strongly vector equilibrium problem for set-valued mappings in real Banach spaces. Using Minty type lemma and KKM-Fan theorem as basic tools, we prove existence theorems for generalized strongly vector equilibrium problem with and without monotonicity, respectively. Some examples are given.

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