Abstract:
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.
Registro:
| Documento: |
Artículo
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| Título: | A note on equivalence of means |
| Autor: | Berrone, L.R.; Lombardi, A.L. |
| Filiación: | Departamento de Matemática, Av. Pellegrini 250, 2000 - Rosario, Argentina
Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina
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| Palabras clave: | Continuous mean; Equivalence; Internal function |
| Año: | 2001
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| Volumen: | 58
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| Número: | 1
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| Página de inicio: | 49
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| Página de fin: | 56
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| Título revista: | Publicationes Mathematicae
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| Título revista abreviado: | Publ. Math.
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| ISSN: | 00333883
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00333883_v58_n1_p49_Berrone |
Referencias:
- Aczél, J., (1966) Lectures on Functional Equations and Their Applications, , Academic Press, New York and London
- Berrone, L.R., Moro, J., On means generated through the Cauchy's mean value theorem Aequationes Math., , to appear
- Borwein, J.M., Borwein, P.B., (1987) Pi and the AGM, , John Wiley & Sons, New York
- Dhombres, J.G., Some recent applications of functional equations (1984) Functional Equations: History, Applications and Theory, pp. 67-91. , (J. Aczél, ed.), D. Reidel, Dordrecht
- Bullen, P.S., Mitrinović, D.S., Vasić, P.M., (1988) Means and Their Inequalities, , D. Reidel, Dordrecht
- Pietra, G., Di una formula per il calcolo delle medie combinatorie (1939) Attn. Soc. Progr. Sci., 27 (5), pp. 38-45
Citas:
---------- APA ----------
Berrone, L.R. & Lombardi, A.L.
(2001)
. A note on equivalence of means. Publicationes Mathematicae, 58(1), 49-56.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00333883_v58_n1_p49_Berrone [ ]
---------- CHICAGO ----------
Berrone, L.R., Lombardi, A.L.
"A note on equivalence of means"
. Publicationes Mathematicae 58, no. 1
(2001) : 49-56.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00333883_v58_n1_p49_Berrone [ ]
---------- MLA ----------
Berrone, L.R., Lombardi, A.L.
"A note on equivalence of means"
. Publicationes Mathematicae, vol. 58, no. 1, 2001, pp. 49-56.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00333883_v58_n1_p49_Berrone [ ]
---------- VANCOUVER ----------
Berrone, L.R., Lombardi, A.L. A note on equivalence of means. Publ. Math. 2001;58(1):49-56.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00333883_v58_n1_p49_Berrone [ ]
