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

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...

Full description

Saved in:
Bibliographic Details
Published inJournal of global optimization Vol. 55; no. 1; pp. 27 - 51
Main Authors Ceng, Lu-Chuan, Yao, Jen-Chih
Format Journal Article
LanguageEnglish
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
Online AccessGet full text

Cover

More Information
Summary: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 ).
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-2
content type line 23
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-011-9811-1