Copy
Kazuo HORIUCHI, "A Fixed Point Theorem in Weak Topology for Successively Recurrent System of Set-Valued Mapping Equations and Its Applications" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 10, pp. 2554-2559, October 2009, doi: 10.1587/transfun.E92.A.2554.
Abstract: 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 Xi-1(0) ⊂ Xi-1. Moreover, let us introduce n set-valued mappings Fi : Xi-1 Yi → Fc(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: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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.2554/_p
Copy
@ARTICLE{e92-a_10_2554,
author={Kazuo HORIUCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Fixed Point Theorem in Weak Topology for Successively Recurrent System of Set-Valued Mapping Equations and Its Applications},
year={2009},
volume={E92-A},
number={10},
pages={2554-2559},
abstract={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 Xi-1(0) ⊂ Xi-1. Moreover, let us introduce n set-valued mappings Fi : Xi-1 Yi → Fc(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: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.},
keywords={},
doi={10.1587/transfun.E92.A.2554},
ISSN={1745-1337},
month={October},}
Copy
TY - JOUR
TI - A Fixed Point Theorem in Weak Topology for Successively Recurrent System of Set-Valued Mapping Equations and Its Applications
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2554
EP - 2559
AU - Kazuo HORIUCHI
PY - 2009
DO - 10.1587/transfun.E92.A.2554
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2009
AB - 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 Xi-1(0) ⊂ Xi-1. Moreover, let us introduce n set-valued mappings Fi : Xi-1 Yi → Fc(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: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.
ER -