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January  2008, 4(1): 167-181. doi: 10.3934/jimo.2008.4.167

Semicontinuity of solution mappings of parametric generalized strong vector equilibrium problems

Kenji Kimura 1, and  Jen-Chih Yao 2,

1. 

Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 80424, Taiwan
2. 

Department of Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 80424, Taiwan

Received  November 2006 Revised  July 2007 Published  January 2008

In this paper, we study the $\varepsilon$-generalized strong vector equilibrium problem ($\varepsilon$-GSVEP) and $\varepsilon$-extended vector equilibrium problem ($\varepsilon$-ESVEP) which can be regarded as approximate problems to the generalized strong vector equilibrium problems (GSVEP). Existence results for $\varepsilon$-GSVEP and $\varepsilon$-ESVEP are established. We also investigate various continuities of the solution mappings of $\varepsilon$-GSVEP and $\varepsilon$-ESVEP, respectively.
Keywords: $C$-compactness., $\varepsilon$-generalized vector equilibrium problem, upper semicontinuity, lower semicontinuity.
Mathematics Subject Classification: Primary: 49J40, 49K40; Secondary: 90C3.
Citation: Kenji Kimura, Jen-Chih Yao. Semicontinuity of solution mappings of parametric generalized strong vector equilibrium problems. Journal of Industrial & Management Optimization, 2008, 4 (1) : 167-181. doi: 10.3934/jimo.2008.4.167
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