Bull. Austral. Math. Soc. 72(1) pp.161--172, 2005.
Implicit vector equilibrium problems via nonlinear scalarisation
Jun Li |
Nan-jing Huang |
The first author was supported by the Youth Foundation of Sichuan Education Department of China, the National Natural Science Foundation of Sichuan Education Department of China (2004C018), the Foundation of Sichuan Science and Technology Department of China and the second author was supported by the National Natural Science Foundation of China.
Abstract
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.
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