A Fixed Point Theorem in Weak Topology for Successively Recurrent System of Set-Valued Mapping Equations and Its Applications

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概要

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• Let us introduce n (≥ 2) mappings fi(i = 1, …, n ≡ 0) defined on reflexive real Banach spaces Xi-1 and let fi : Xi-1 → Yi be completely continuous on bounded convex closed subsets $X_{i-1}^{(0)} \\subset X_{i-1}$. Moreover, let us introduce n set-valued mappings $F_i : X_{i-1} \\times Y_i \\to {\\cal F}_c(X_i)$ (the family of all non-empty compact subsets of Xi), (i=1, …, n ≡ 0). Here, we have a fixed point theorem in weak topology on the successively recurrent system of set-valued mapping equations: xi ∈ Fi(xi-1, fi(xi-1)), (i=1, …, n ≡ 0). This theorem can be applied immediately to analysis of the availability of system of circular networks of channels undergone by uncertain fluctuations and to evaluation of the tolerability of behaviors of those systems.

• 2009-10-01

著者

• Horiuchi Kazuo

  Emeritus Of Waseda University With The Advanced Research Institute For Science And Engineering Wased

関連論文

• A Fixed Point Theorem in Weak Topology for Successively Recurrent System of Set-Valued Mapping Equations and Its Applications

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