Summary
International Symposium on Nonlinear Theory and its Applications
2008
Session Number:B4L-F
Session:
Number:B4L-F3
A Fixed Point Theorem for Successively Recurrent System of Set-Valued Mapping Equations and its Applications
Kazuo HORIUCHI,
pp.-
Publication Date:2008/9/7
Online ISSN:2188-5079
Summary:
Let us introduce n (? 2) mappings fi (i = 1, 2, . . . , n ≡ 0) defined on Banach spaces Xi?1 (i = 1, 2, . . . , n ≡ 0), respectively, and let fi : Xi?1 → Yi be completely continuous on bounded convex closed subsets X(0)i?1⊂ Xi?1 . Moreover, let us introduce n set-valued mappings Fi : Xi?1 × Yi → F (Xi )(the family of all non-empty compact subsets of Xi ), (i = 1, 2, . . . , n ≡ 0). Here, we have a fixed point theorem on the successively recurrent system of set-valued mapping equations:xi ∈ Fi (xi?1, fi (xi?1 )),(i = 1, 2, . . . , 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. In this paper, mathematical situation and detailed proof in weak topology are discussed, about this theorem.