Existence theorems for generalized set-valued mixed (quasi-)variational inequalities in Banach spaces

• Published in: Journal of global optimization Vol. 55; no. 1; pp. 27 - 51
• Main Authors: Ceng, Lu-Chuan, Yao, Jen-Chih
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.01.2013; Springer; Springer Nature B.V
• Subjects: Banach space; Banach spaces; Computer Science; Existence theorems; Game theory; Inequalities; Inequality; Mathematics; Mathematics and Statistics; Nonlinearity; Operations Research/Decision Theory; Operators; Optimization; Real Functions; Theorems; Mixed variational inequality; Mixed quasi-variational inequality; KKM theorem; projection operator; 49J40; 47H09; Upper semicontinuousset-valued mapping; Generalized; Kakutani–Fan–Glicksberg fixed point theorem; 47H17; Composite mapping

In this paper, utilizing the properties of the generalized f -projection operator and the well-known KKM and Kakutani–Fan–Glicksberg theorems, under quite mide assumptions, we derive some new existence theorems for the generalized set-valued mixed variational inequality and the generalized set-value...