数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1179-1192.doi: 10.1016/S0252-9602(14)60078-3

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EKELAND´S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS

龚循华   

  1. Department of Mathematics, Nanchang University, Nanchang 330031, China
  • 收稿日期:2013-01-30 修回日期:2013-10-08 出版日期:2014-07-20 发布日期:2014-07-20
  • 基金资助:

    This research was partially supported by the National Natural Science Foundation of China (11061023).

EKELAND´S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS

 GONG Xun-Hua   

  1. Department of Mathematics, Nanchang University, Nanchang 330031, China
  • Received:2013-01-30 Revised:2013-10-08 Online:2014-07-20 Published:2014-07-20
  • Supported by:

    This research was partially supported by the National Natural Science Foundation of China (11061023).

摘要:

In this paper, we introduce a concept of quasi C-lower semicontinuity for set-valued mapping and provide a vector version of Ekeland´s theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient so-lution for set-valued vector equilibrium problems without the assumption of convexity of the
constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of "-approximate solution for set-valued vector equi-librium problems without the assumptions of compactness and convexity of the constraint set.

关键词: Ekeland´s principle, set-valued vector equilibrium problems, weakly efficient solution, "-approximate solution, existence

Abstract:

In this paper, we introduce a concept of quasi C-lower semicontinuity for set-valued mapping and provide a vector version of Ekeland´s theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient so-lution for set-valued vector equilibrium problems without the assumption of convexity of the
constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of "-approximate solution for set-valued vector equi-librium problems without the assumptions of compactness and convexity of the constraint set.

Key words: Ekeland´s principle, set-valued vector equilibrium problems, weakly efficient solution, "-approximate solution, existence

中图分类号: 

  • 49J52