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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:
54H25Fixed-point and coincidence theorems in topological spaces
54C60Set-valued maps (general topology)
91B52Special types of equilibria in economics
91A06n-person games, n>2
91A44Games involving topology or set theory
47J22Variational and other types of inclusions