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...

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Detalles Bibliográficos
Autores principales: Berrone, L.R., Lombardi, A.L.
Formato: JOUR
Materias:
Continuous mean
Equivalence
Internal function
Acceso en línea: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 todo:paper_00333883_v58_n1_p49_Berrone
record_format dspace
spelling todo:paper_00333883_v58_n1_p49_Berrone2023-10-03T14:45:37Z A note on equivalence of means Berrone, L.R. Lombardi, A.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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Berrone, L.R.
Lombardi, A.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.
format JOUR
author Berrone, L.R.
Lombardi, A.L.
author_facet Berrone, L.R.
Lombardi, A.L.
author_sort Berrone, L.R.
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
url http://hdl.handle.net/20.500.12110/paper_00333883_v58_n1_p49_Berrone
work_keys_str_mv AT berronelr anoteonequivalenceofmeans
AT lombardial anoteonequivalenceofmeans
AT berronelr noteonequivalenceofmeans
AT lombardial noteonequivalenceofmeans
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