The search functionality is under construction.
The search functionality is under construction.

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

Kazuo HORIUCHI

  • Full Text Views

    0

  • Cite this

Summary :

Let us introduce n ( ≥ 2) mappings fi (i=1,,n ≡ 0) defined on reflexive real Banach spaces Xi-1 and let fi:Xi-1Yi be completely continuous on bounded convex closed subsets Xi-1(0)Xi-1. Moreover, let us introduce n set-valued mappings Fi : Xi-1 YiFc(Xi) (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:xiFi(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.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.10 pp.2554-2559
Publication Date
2009/10/01
Publicized
Online ISSN
1745-1337
DOI
10.1587/transfun.E92.A.2554
Type of Manuscript
Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category
Nonlinear Problems

Authors

Keyword