Open AccessCollectively fixed point theorems in noncompact abstract convex spaces with applications
Author(s) -
Haishu Lu,
Kai Zhang,
Rong Li
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021718
Subject(s) - mathematics , intersection (aeronautics) , convexity , fixed point theorem , regular polygon , pure mathematics , fixed point , nash equilibrium , space (punctuation) , combinatorics , discrete mathematics , mathematical economics , mathematical analysis , computer science , geometry , financial economics , engineering , economics , aerospace engineering , operating system
In this paper, by using the KKM theory and the properties of $ \Gamma $-convexity and $ {\frak{RC}} $-mapping, we investigate the existence of collectively fixed points for a family with a finite number of set-valued mappings on the product space of noncompact abstract convex spaces. Consequently, as applications, some existence theorems of generalized weighted Nash equilibria and generalized Pareto Nash equilibria for constrained multiobjective games, some nonempty intersection theorems with applications to the Fan analytic alternative formulation and the existence of Nash equilibria, and some existence theorems of solutions for generalized weak implicit inclusion problems in noncompact abstract convex spaces are given. The results obtained in this paper extend and generalize many corresponding results of the existing literature.