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April  2008, 4(2): 313-327. doi: 10.3934/jimo.2008.4.313

Well-posedness for parametric vector equilibrium problems with applications

Kenji Kimura 1, , Yeong-Cheng Liou 2, , Soon-Yi Wu 3, and  Jen-Chih Yao 4,

1. 

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

Department of Information Management, Cheng Shiu University, No.840, Chengcing Rd., Niaosong Township, Kaohsiung County 833, Taiwan, R.O.C.
3. 

Department of Mathematics, National Cheng Kung University, Tainan, 701, Taiwan, National Center for Theoretical Sciences, Taiwan
4. 

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

Received  January 2007 Revised  December 2007 Published  April 2008

In this paper, we study the parametric well-posedness for vector equilibrium problems and propose a generalized well-posed concept for equilibrium problems with equilibrium constraints (EPEC in short) in topological vector spaces setting. We show that under suitable conditions, the well-posedness defined by approximating solution nets is equivalent to the upper semicontinuity of the solution mapping of perturbed problems. Further, since optimization problems and variational inequality problems are special cases of equilibrium problems, related variational problems can be adopted under some equivalent conditions. Finally, we also study the relationship between well-posedness and parametric well-posedness.
Keywords: convexity., Vector equilibrium problem, upper-semicontinuous, well-posedness.
Mathematics Subject Classification: 46A40, 47H14, 49J, 54C60, 54C08,90C, 65.
Citation: Kenji Kimura, Yeong-Cheng Liou, Soon-Yi Wu, Jen-Chih Yao. Well-posedness for parametric vector equilibrium problems with applications. Journal of Industrial & Management Optimization, 2008, 4 (2) : 313-327. doi: 10.3934/jimo.2008.4.313
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