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dc.contributor.author
Berrone, Lucio Renato
dc.date.available
2017-02-24T19:08:23Z
dc.date.issued
2015-11
dc.identifier.citation
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
dc.identifier.issn
1422-6383
dc.identifier.uri
http://hdl.handle.net/11336/13390
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Functional Equations
dc.subject
Cauchy Difference
dc.subject
Means
dc.subject
P-Means
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
P-means and the solution of a functional equation involving Cauchy differences
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-02-23T13:54:06Z
dc.identifier.eissn
1420-9012
dc.journal.volume
68
dc.journal.number
3
dc.journal.pagination
375–393
dc.journal.pais
Suiza
dc.journal.ciudad
Basilea
dc.description.fil
Fil: Berrone, Lucio Renato. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingenieria y Agrimensura. Escuela de Ingenieria Electrónica. Laboratorio de Acústica y Electroacústica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentina
dc.journal.title
Results In Mathematics
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00025-015-0446-2
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00025-015-0446-2
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