The fixed point and the common fixed point properties in finite pseudo-ordered sets

Abstract: In this paper, we first prove that every finite nonempty pseudo-ordered with a least element has the least fixed point property and the least common fixed point property for every finite commutative family of self monotone maps. Dually, we establish that a finite nonempty pseudo-ordered wi...

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Autor principal: Stouti,Abdelkader
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2018
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Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100001
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spelling oai:scielo:S0716-091720180001000012018-03-13The fixed point and the common fixed point properties in finite pseudo-ordered setsStouti,Abdelkader Pseudo-ordered set trellis complete trellis monotone map fixed point property least fixed point property greatest fixed point property common fixed point property. Abstract: In this paper, we first prove that every finite nonempty pseudo-ordered with a least element has the least fixed point property and the least common fixed point property for every finite commutative family of self monotone maps. Dually, we establish that a finite nonempty pseudo-ordered with a greatest element has the greatest fixed point property and the greatest common fixed point property for every finite commutative family of self monotone maps. Secondly, we prove that every monotone map ƒ defined on a nonempty finite pseudo-ordered (X, ⊵) has at least a fixed point if and only if there is at least an element ɑ of X such that the subset of X defined by {ƒn(ɑ) : n ∈ ℕ } has a least or a greatest element. Furthermore, we show that the set of all common fixed points of every finite commutative family of monotone maps defined on a finite nonempty complete trellis is also a nonempty complete trellis.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.37 n.1 20182018-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100001en10.4067/S0716-09172018000100001
institution Scielo Chile
collection Scielo Chile
language English
topic Pseudo-ordered set
trellis
complete trellis
monotone map
fixed point property
least fixed point property
greatest fixed point property
common fixed point property.
spellingShingle Pseudo-ordered set
trellis
complete trellis
monotone map
fixed point property
least fixed point property
greatest fixed point property
common fixed point property.
Stouti,Abdelkader
The fixed point and the common fixed point properties in finite pseudo-ordered sets
description Abstract: In this paper, we first prove that every finite nonempty pseudo-ordered with a least element has the least fixed point property and the least common fixed point property for every finite commutative family of self monotone maps. Dually, we establish that a finite nonempty pseudo-ordered with a greatest element has the greatest fixed point property and the greatest common fixed point property for every finite commutative family of self monotone maps. Secondly, we prove that every monotone map ƒ defined on a nonempty finite pseudo-ordered (X, ⊵) has at least a fixed point if and only if there is at least an element ɑ of X such that the subset of X defined by {ƒn(ɑ) : n ∈ ℕ } has a least or a greatest element. Furthermore, we show that the set of all common fixed points of every finite commutative family of monotone maps defined on a finite nonempty complete trellis is also a nonempty complete trellis.
author Stouti,Abdelkader
author_facet Stouti,Abdelkader
author_sort Stouti,Abdelkader
title The fixed point and the common fixed point properties in finite pseudo-ordered sets
title_short The fixed point and the common fixed point properties in finite pseudo-ordered sets
title_full The fixed point and the common fixed point properties in finite pseudo-ordered sets
title_fullStr The fixed point and the common fixed point properties in finite pseudo-ordered sets
title_full_unstemmed The fixed point and the common fixed point properties in finite pseudo-ordered sets
title_sort fixed point and the common fixed point properties in finite pseudo-ordered sets
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2018
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100001
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