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
Materias:	Pseudo-ordered set trellis complete trellis monotone map fixed point property least fixed point property greatest fixed point property common fixed point property.
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
work_keys_str_mv	AT stoutiabdelkader thefixedpointandthecommonfixedpointpropertiesinfinitepseudoorderedsets AT stoutiabdelkader fixedpointandthecommonfixedpointpropertiesinfinitepseudoorderedsets
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The fixed point and the common fixed point properties in finite pseudo-ordered sets

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