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Implicit vector equilibrium problems via nonlinear scalarisation

Published online by Cambridge University Press:  17 April 2009

Jun Li  and
Nan-Jing Huang
Jun Li
Affiliation:
School of Mathematics and Information, China West Normal University, Nanchong, Sichuan 637002, Peoples Republic of China
Nan-Jing Huang
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, Peoples Republic of China, e-mail: nanjinghuang@hotmail.com, njhuang@scu.edu.cn
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The purpose of this paper is to introduce a nonlinear scalarisation function for solving a class of implicit vector equilibrium problems. We prove a scalarisation lemma to show the relation between the implicit vector equilibrium problem and the nonlinear scalarisation function. Then we derive some new existence theorems for solutions of implicit vector equilibrium problems, using the scalarisation lemma and the FKKM theorem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 1 , August 2005 , pp. 161 - 172
Copyright
Copyright © Australian Mathematical Society 2005

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