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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Universidad Católica del Norte, Departamento de Matemáticas
2018
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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 |
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Scielo Chile |
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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. |
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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 |
_version_ |
1718439831048028160 |