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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2001
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| 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 |
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| 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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