Existence results for system of variational inequality problems with semimonotone operators.
Plubtieng, Somyot, Sombut, Kamonrat (2010)
Journal of Inequalities and Applications [electronic only]
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Plubtieng, Somyot, Sombut, Kamonrat (2010)
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Paolo Cubiotti (1996)
Commentationes Mathematicae Universitatis Carolinae
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In this note we prove that some recent results on an implicit variational inequality problem for multivalued mappings, which seem to extend and improve some well-known and celebrated results, are not correct.
Ya-Ping Liu, Ya-Yong Tang, Nan-Jing Huang, Yeol Je Cho (1998)
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Liu, Zeqing, Sun, Juhe, Shim, Soo Hak, Kang, Shin Min (2005)
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Liu, Zeqing, Gao, Haiyan, Kang, Shin Min, Shim, Soo Hak (2006)
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Noor, Muhammad Aslam (2009)
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Noor, Muhammad Aslam (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Ching-Yan Lin, Liang-Ju Chu (2003)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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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...