Acta mathematica scientia, Series B >
EKELAND´S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS
Received date: 2013-01-30
Revised date: 2013-10-08
Online published: 2014-07-20
Supported by
This research was partially supported by the National Natural Science Foundation of China (11061023).
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.
GONG Xun-Hua . EKELAND´S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1179 -1192 . DOI: 10.1016/S0252-9602(14)60078-3
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