# Variational inequalities in noncompact nonconvex regions

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

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

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topChing-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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