Variational inequalities in noncompact nonconvex regions

Ching-Yan Lin; Liang-Ju Chu

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2003)

  • Volume: 23, Issue: 1, page 5-19
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Ching-Yan Lin, and Liang-Ju Chu. "Variational inequalities in noncompact nonconvex regions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 23.1 (2003): 5-19. <http://eudml.org/doc/271511>.

@article{Ching2003,
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.},
author = {Ching-Yan Lin, Liang-Ju Chu},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {Nikaidô's coincidence theorem; variational inequality; nearly convex; V₀-Karamardian condition; Saigal condition; acyclic multifunction; algebraic interior; bounding points; variational inequalities; coincidence theorem; convergence criteria},
language = {eng},
number = {1},
pages = {5-19},
title = {Variational inequalities in noncompact nonconvex regions},
url = {http://eudml.org/doc/271511},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Ching-Yan Lin
AU - Liang-Ju Chu
TI - Variational inequalities in noncompact nonconvex regions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2003
VL - 23
IS - 1
SP - 5
EP - 19
AB - 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.
LA - eng
KW - Nikaidô's coincidence theorem; variational inequality; nearly convex; V₀-Karamardian condition; Saigal condition; acyclic multifunction; algebraic interior; bounding points; variational inequalities; coincidence theorem; convergence criteria
UR - http://eudml.org/doc/271511
ER -

References

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  12. [12] L.J. Lin, Pre-Vector variational inequalities, Bull. Australian Math. Soc. 53 (1995), 63-70. Zbl0858.49008
  13. [13] G.J. Minty, On the maximal domain of a monotone function, Michigan Math. J. 8 (1961), 135-137. Zbl0102.37503
  14. [14] H. Nikaidô, Coincidence and some systems of inequalities, J. Math. Soc., Japan 11 (1959), 354-373. Zbl0096.08004
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  16. [16] R. Saigal, Extension of the generalized complemetarity problem, Math. of Oper. Res. 1 (3) (1976), 260-266. Zbl0363.90091

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