林强.关于集值系统x∈F(x,y),y∈G(x,y)解的存在性[J].数学研究及应用,1992,12(1):33~36
关于集值系统x∈F(x,y),y∈G(x,y)解的存在性
On Existence of Solution for the Set-Valued System x∈F(x,y),y∈G(x,y)
投稿时间:1990-02-10  
DOI:10.3770/j.issn:1000-341X.1992.01.005
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英文关键词:
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作者单位
林强 哈尔滨电工学院数学教研室 
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中文摘要:
      
英文摘要:
      Let (E, ‖·‖) be a uniformly convex Banach space, X a nonempty compact and convex subset of E. Let F be a closed mapping of X×X into 2X, G a mapping of X×X into C(X). It is shown that if for any f∈C(X), x∈X, F(x,f(x)) is a closed and convex subset of X, and G(x,f(x)) is a continuous function and for any x,y1,y2∈X,H(x,G(x,y1),G(x,y2))≤‖y1-y2‖ then there exist X0,y0∈X such that X0∈F(x0,y0) and y0∈G(x0, y0).
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