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
Descripción
Sumario: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.

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