Connectedness of approximate solutions set for vector equilibrium problems in Hausdorff topological vector spaces

Fixexd point theory and applications

Zhi-bin Liu¹  Nan-jing Huang²  Bin Chen²  Qing-you Liu³ 

[1] Department of Applied Mathematics, Southwest Petroleum University, Chengdu, PR China;Department of Mathematics, Sichuan University, Chengdu, P.R. China;State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, PR China

关键词: vector equilibrium problem;    scalarization method;    ε-weak efficient solution;    ε-efficient solution;    connectedness;   

DOI  :  10.1186/1687-1812-2011-36

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, a scalarization result of ε-weak efficient solution for a vector equilibrium problem (VEP) is given. Using this scalarization result, the connectedness of ε-weak efficient and ε-efficient solutions sets for the VEPs are proved under some suitable conditions in real Hausdorff topological vector spaces. The main results presented in this paper improve and generalize some known results in the literature.

【 授权许可】

CC BY