Existence of Solutions and Star-shapedness in Generalized Minty Variational Inequalities in Banach Spaces
نویسندگان
چکیده
The purpose of this paper is to introduce and study Generalized Minty Variational Inequalities in Banach spaces. We consider a problem of vector variational inequalities, referred as Generalized Minty VI(f ′ − , K), in a real Banach space X, where K is a nonempty subset of X and f ′ − is the lower Dini directional derivative of a real function f defined on an open set in X containing K. The results presented in this paper generalize the corresponding results of Giovanni P. Crespi, Ivan Ginchev and Matteo Rocca [Giovanni P. Crespi, Ivan Ginchev and Matteo Rocca, Existence of solutions and star-shapedness in Minty Variational Inequalities, Journal of Global Optimization (2005), 32, 485-494]. 2000 Mathematics Subject Classification: 90C99, 74P99
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Existence of Solutions and Star-shapedness in Minty Variational Inequalities
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