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

Lu-Chuan Ceng () and Jen-Chih Yao ()

Journal of Global Optimization, 2013, vol. 55, issue 1, 27-51

Abstract: 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-valued mixed quasi-variational inequality in reflexive and smooth Banach spaces, respectively. The results presented in this paper can be viewed as the supplement, improvement and extension of recent results in Wu and Huang (Nonlinear Anal 71:2481–2490, 2009 ). Copyright Springer Science+Business Media, LLC. 2013

Keywords: Generalized f -projection operator; Mixed variational inequality; Mixed quasi-variational inequality; Upper semicontinuousset-valued mapping; Composite mapping; KKM theorem; Kakutani–Fan–Glicksberg fixed point theorem; 49J40; 47H09; 47H17 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-011-9811-1

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