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ArticleOriginal scientific text

Title

Variational inequalities in noncompact nonconvex regions

Authors 1, 2

Affiliations

  1. Center for General Education, National Taipei University of Technology, Taipei, Taiwan, Republic of China
  2. Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, Republic of China

Abstract

In this paper, a general existence theorem on the generalized variational inequality problem GVI(T,C,ϕ) is derived by using our new versions of Nikaidô's coincidence theorem, for the case where the region C is noncompact and nonconvex, but merely is a nearly convex set. Equipped with a kind of V₀-Karamardian condition, this general existence theorem contains some existing ones as special cases. Based on a Saigal condition, we also modify the main theorem to obtain another existence theorem on GVI(T,C,ϕ), which generalizes a result of Fang and Peterson.

Keywords

ENG
Nikaidô's coincidence theorem, variational inequality, nearly convex, V₀-Karamardian condition, Saigal condition, acyclic multifunction, algebraic interior, bounding points

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2003/23/1
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Pages:
5-19
Main language of publication
English
Received
2002-10-25
Published
2003

DOI: 10.7151/dmgt.1042

Exact and natural sciences