Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2011; 48(6): 1225-1233

Printed November 1, 2011

https://doi.org/10.4134/BKMS.2011.48.6.1225

Copyright © The Korean Mathematical Society.

Connectedness and compactness of weak efficient solutions for vector equilibrium problems

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