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...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Stouti,Abdelkader
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2018
Materias:
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100001
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
Descripción
Sumario: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.