A note on equivalence of means

Given a real interval I, a relation, denoted by '∼', is defined on the set of means on I x I by setting M ∼ N when there exists a surjective continuous function f solving the functional equation f(M(x,y)) = N(f (x),f(y)), x,y ∈ I . A surjective and continuous solution to this equation turn...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Lombardi, Ariel L.
Publicado: 2001
Materias:
Continuous mean
Equivalence
Internal function
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00333883_v58_n1_p49_Berrone
http://hdl.handle.net/20.500.12110/paper_00333883_v58_n1_p49_Berrone
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00333883_v58_n1_p49_Berrone
record_format dspace
spelling paper:paper_00333883_v58_n1_p49_Berrone2023-06-08T15:00:28Z A note on equivalence of means Lombardi, Ariel L. Continuous mean Equivalence Internal function Given a real interval I, a relation, denoted by '∼', is defined on the set of means on I x I by setting M ∼ N when there exists a surjective continuous function f solving the functional equation f(M(x,y)) = N(f (x),f(y)), x,y ∈ I . A surjective and continuous solution to this equation turns out to be injective and so, '∼' is an equivalence. This fact seems to be not properly noticed in the literature on means. Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2001 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00333883_v58_n1_p49_Berrone http://hdl.handle.net/20.500.12110/paper_00333883_v58_n1_p49_Berrone
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Continuous mean
Equivalence
Internal function
spellingShingle Continuous mean
Equivalence
Internal function
Lombardi, Ariel L.
A note on equivalence of means
topic_facet Continuous mean
Equivalence
Internal function
description Given a real interval I, a relation, denoted by '∼', is defined on the set of means on I x I by setting M ∼ N when there exists a surjective continuous function f solving the functional equation f(M(x,y)) = N(f (x),f(y)), x,y ∈ I . A surjective and continuous solution to this equation turns out to be injective and so, '∼' is an equivalence. This fact seems to be not properly noticed in the literature on means.
author Lombardi, Ariel L.
author_facet Lombardi, Ariel L.
author_sort Lombardi, Ariel L.
title A note on equivalence of means
title_short A note on equivalence of means
title_full A note on equivalence of means
title_fullStr A note on equivalence of means
title_full_unstemmed A note on equivalence of means
title_sort note on equivalence of means
publishDate 2001
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00333883_v58_n1_p49_Berrone
http://hdl.handle.net/20.500.12110/paper_00333883_v58_n1_p49_Berrone
work_keys_str_mv AT lombardiariell anoteonequivalenceofmeans
AT lombardiariell noteonequivalenceofmeans
_version_ 1768545364214808576

Ejemplares similares