Connectedness and compactness of weak efficient solutions for vector equilibrium problems
Bull. Korean Math. Soc. 2011 Vol. 48, No. 6, 1225-1233
https://doi.org/10.4134/BKMS.2011.48.6.1225
Published online November 1, 2011
Xian Jun Long and Jian Wen Peng
Chongqing Technology and Business University, Chongqing Normal University
Abstract : In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. $\bf 133$ (2007), 151--161].
Keywords : vector equilibrium problem, weak efficient solution, scalarization, existence, connectedness
MSC numbers : 49J40, 90C31
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