On fixed point approach to equilibrium problem

The equilibrium problem defined by the Nikaidô–Isoda–Fan inequality contains a number of problems such as optimization, variational inequality, Kakutani fixed point, Nash equilibria, and others as special cases. This paper presents a picture for the relationship between the fixed points of the Morea...

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Bibliographic Details
Published inJournal of fixed point theory and applications Vol. 23; no. 4
Main Authors Muu, Le Dung, Le, Xuan Thanh
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.11.2021
Subjects
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
47H10
Monotone equilibria
47H05
fixed point
Moreau proximal mapping
90C33
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Summary:The equilibrium problem defined by the Nikaidô–Isoda–Fan inequality contains a number of problems such as optimization, variational inequality, Kakutani fixed point, Nash equilibria, and others as special cases. This paper presents a picture for the relationship between the fixed points of the Moreau proximal mapping and the solutions of the equilibrium problem that satisfies some kinds of monotonicity and Lipschitz-type condition.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-021-00890-0