[9]. Several equivalent forms are then formulated and one of them, the maximal element version, is used to obtain a fixed point theorem which in turn is applied to obtain an existence theorem of an equilibrium point in a one-person game. Next, by applying the minimax inequality, we present some fixed point theorems for set-valued inward and outward mappings on a non-compact convex set in a topological vector space. These results generalize the corresponding results due to Browder
In this paper, we first prove an improved version of the selection theorem of Yannelis-Prabhakar and next prove a fixed point theorem in a non-compact product space. As applications, an intersection theorem and two equilibrium existence theorems for a non-compact abstract economy are given.
Let I be a finite or infinite index set, X be a topological space and (Y i , {ϕ N i }) i∈I be a family of finitely continuous topological spaces (in short, FC-space). For each i ∈ I , let A i : X → 2 Y i be a set-valued mapping. Some existence theorems of maximal elements for the family {A i } i∈I are established under noncompact setting of FC-spaces. As applications, some equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in noncompact FC-spaces. These theorems improve, unify and generalize many important results in recent literature. 2004 Elsevier Inc. All rights reserved.
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