Abstract
This paper aims to introduce a new kind of Variational Inequality, i.e. a ‘Generalized Vector Variational-Like Inequality’ which includes several classic and well-known Variational Inequalities as special cases. As an application of the Knaster-Kuratowski-Mazurkiewicz principle - in the extended form given by Fan in 1961 -, we prove that there exist solutions for our Generalized Vector Variational-Like Inequality under reasonable hypotheses. These results generalize corresponding results given by Chen et al. in (1992), Giannessi (1980), Harker and Pang (1990), Hartman and Stampacchia (1966), Isac (1990), Lee et al. (1993), Noor (1988), Saigal (1976), Siddiqi et al. (1995) and Yang (1993).
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Chang, SS., Thompson, H.B., Yuan, G.XZ. (2000). Existence of Solutions for Generalized Vector Variational-Like Inequalities. In: Giannessi, F. (eds) Vector Variational Inequalities and Vector Equilibria. Nonconvex Optimization and Its Applications, vol 38. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0299-5_3
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DOI: https://doi.org/10.1007/978-1-4613-0299-5_3
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