EKELAND´S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS

doi:10.1016/S0252-9602(14)60078-3

Abstract

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

CLC Number:

49J52

GONG Xun-Hua. EKELAND´S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS[J].Acta mathematica scientia,Series B, 2014, 34(4): 1179-1192.

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