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GENERALIZED IMPLICIT INCLUSION PROBLEMS ON NONCOMPACT SETS WITH APPLICATIONS

Part of: Existence theories

Published online by Cambridge University Press:  15 March 2011

SAN-HUA WANG  and
NAN-JING HUANG
SAN-HUA WANG
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China Department of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, PR China
NAN-JING HUANG*
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China (email: nanjinghuang@hotmail.com)
*
✉For correspondence; e-mail: nanjinghuang@hotmail.com
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Abstract

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In this paper, a class of generalized implicit inclusion problems is introduced, which can be regarded as a generalization of variational inequality problems, equilibrium problems, optimization problems and inclusion problems. Some existence results of solutions for such problems are obtained on noncompact subsets of Hausdorff topological vector spaces using the famous FKKM theorem. As applications, some existence results for vector equilibrium problems and vector variational inequalities on noncompact sets of Hausdorff topological vector spaces are given.

Keywords

generalized implicit inclusion problemnoncompact setFKKM theoremvector equilibrium problemvector variational inequality

MSC classification

Secondary: 49J40: Variational methods including variational inequalities
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 261 - 279
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

This work was supported by the National Natural Science Foundation of China (70831005, 10671135) and the Natural Science Foundation of Jiangxi Province (2007GZS2120).

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