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Collective fixed points, generalized games and systems of generalized quasi-variational inclusion problems in topological spaces. (English) Zbl 1229.54054

Summary: In this paper, by using a fixed point theorem for expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces due to the author [X. P. Ding, Nonlinear Anal., Theory Methods Appl. 70, No. 2, A, 881–889 (2009; Zbl 1170.54015)], we first prove a collective fixed point theorem and an existence theorem of equilibrium points for a generalized game. As applications, some new existence theorems of solutions for systems of generalized quasi-variational inclusion problems are established in noncompact topological spaces. Our results are different from known results in the literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54C60 Set-valued maps in general topology
91B52 Special types of economic equilibria
91A06 \(n\)-person games, \(n>2\)
91A44 Games involving topology, set theory, or logic
47J22 Variational and other types of inclusions

Citations:

Zbl 1170.54015
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Full Text: DOI

References:

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