scholarly journals Lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem

2014 ◽  
Vol 10 (4) ◽  
pp. 1225-1234 ◽  
Author(s):  
Qilin Wang ◽  
◽  
Shengji Li ◽  
Keyword(s):  
Equilibrium Problem ◽  
Lower Semicontinuity ◽  
Vector Equilibrium Problem ◽  
Generalized Vector Equilibrium Problem ◽  
Solution Mapping ◽  
Vector Equilibrium

scholarly journals Lower semicontinuity of approximate solution mappings for a parametric generalized strong vector equilibrium problem

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1641-1648
Author(s):  
Qilin Wang ◽  
Liu He ◽  
Xiaobing Li
Keyword(s):  
Approximate Solution ◽  
Equilibrium Problem ◽  
Lower Semicontinuity ◽  
Vector Equilibrium Problem ◽  
Convex Mappings ◽  
Solution Mapping ◽  
Vector Equilibrium ◽  
Approximate Solution Mapping ◽  
Strong Vector Equilibrium Problem

In this paper, by using a property of convex mappings, one establishes the lower semicontinuity of the approximate solution mapping to a parametric generalized strong vector equilibrium problem without these assumptions about monotonicity and compactness. Our proof approach is different from the ones in the literature.

scholarly journals LOWER SEMICONTINUITY OF PARAMETRIC GENERALIZED WEAK VECTOR EQUILIBRIUM PROBLEMS

2009 ◽  
Vol 81 (1) ◽  
pp. 85-95 ◽  
Author(s):  
SHENG-JIE LI ◽  
HUI-MIN LIU ◽  
CHUN-RONG CHEN
Keyword(s):  
Equilibrium Problem ◽  
Lower Semicontinuity ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Vector Equilibrium Problems ◽  
Solution Mapping ◽  
Scalarization Method ◽  
Set Valued Mappings ◽  
Vector Equilibrium ◽  
Weak Vector

AbstractIn this paper, using a scalarization method, we obtain sufficient conditions for the lower semicontinuity and continuity of the solution mapping to a parametric generalized weak vector equilibrium problem with set-valued mappings.

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.

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