Artículo
P-means and the solution of a functional equation involving Cauchy differences
Fecha de publicación:
11/2015
Editorial:
Springer
Revista:
Results In Mathematics
ISSN:
1422-6383
e-ISSN:
1420-9012
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Solutions to the functional equation
f(x+y)−f(x)−f(y)=2f(Φ(x,y)),x,y>0,
are sought for the admissible pairs (f,Φ)(f,Φ) constituted by a strictly monotonic function f and a strictly increasing in both variables mean ΦΦ . A related class of means, P-means, is introduced, studied and then employed in solving (1) under additional hypotheses on ΦΦ . For instance, Ger has proved that the unique P-mean which is also quasiarithmetic is the geometric mean G(x,y)=xy−−√G(x,y)=xy . An elementary proof to this result is given in this paper. Moreover, as a consequence of a fundamental result on the uniqueness of representation of P-means it is proved that the geometric mean G is the unique homogeneous P-mean.
Palabras clave:
Functional Equations
,
Cauchy Difference
,
Means
,
P-Means
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(CCT - ROSARIO)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - ROSARIO
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - ROSARIO
Citación
Berrone, Lucio Renato; P-means and the solution of a functional equation involving Cauchy differences; Springer; Results In Mathematics; 68; 3; 11-2015; 375–393
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