Generalized Cauchy means

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• 作者：Lucio R. Berrone
• 刊名：Aequationes Mathematicae
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：90
• 期：2
• 页码：307-328
• 全文大小：586 KB
• 参考文献：1.Aczél J.: Lectures on Functional Equations and their Applications. Academic Press, New York (1966)MATH
  2.Berrone L.R.: Decreasing sequences of means appearing from non-decreasing functions. Publ. Math. Debrecen 55(1–2), 53–72 (1999)MathSciNet MATH
  3.Berrone L.: Invariance of the Cauchy mean value expression with an application to the problem of equality of Cauchy means. Internat. J. Math. Math. Sci. 2005(18), 2895–2912 (2005)MathSciNet CrossRef MATH
  4.Berrone L.R.: A dynamical characterization of quasilinear means. Aequationes Math. 84(1), 51–70 (2012)MathSciNet CrossRef MATH
  5.Berrone, L.R., Lombardi, A.L.: A note on equivalence of means. Publ. Math. Debrecen 58, Fasc. 1–2, 49-56 (2001)
  6.Berrone L.R., Moro J.: Lagrangian means. Aequationes Math. 55, 217–226 (1998)MathSciNet CrossRef MATH
  7.Berrone L.R., Moro J.: Cauchy means. Aequationes Math. 60, 1–14 (2000)MathSciNet CrossRef MATH
  8.Bullen P.S.: Handbook of Means and their Inequalities. Series Mathematics and its Applications. 2nd ed. Kluwer Academic Publisher, London (2003)CrossRef MATH
  9.Hardy G., Littlewood J.E., Pólya G.: Inequalities, 1st ed. Cambridge Univ. Press, Cambridge (1934)MATH
  10.Matkowski J.: Solution of a regularity problem in equality of Cauchy means. Publ. Math. Debrecen 64(3–4), 391–400 (2004)MathSciNet MATH
  11.Matkowski J.: Generalized weighted quasi-arithmetic means. Aequationes Math. 79, 203–212 (2010)MathSciNet CrossRef MATH
  12.Losonczi L.: Equality of two variable weighted means: reduction to differential equations. Aequationes Math. 58(3), 223–241 (1999)MathSciNet CrossRef MATH
  13.Losonczi L.: Equality of Cauchy means values. Publ. Math. Debrecen 57(1–2), 217–230 (2000)MathSciNet MATH
  14.Losonczi L.: Equality of two variable Cauchy mean values. Aequationes Math. 65(1–2), 61–81 (2003)MathSciNet MATH
  
• 作者单位：Lucio R. Berrone (1)
  
  1. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Laboratorio de Acústica y Electroacústica, Facultad de Cs. Exactas, Ing. y Agrim., Univ. Nac. de Rosario, Riobamba 245 bis, 2000, Rosario, Argentina
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Combinatorics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8903

文摘

Given two means M and N, the operator \({\mathcal{M}_{M,N}}\) assigning to a given mean μ the mean $$\mathcal{M}_{M,N}(\mu )(x,y)=M(\mu (x,N(x,y)),\mu (N(x,y),y))$$was defined in Berrone and Moro (Aequationes Math 60:1–14, 2000) in connection with Cauchy means: the Cauchy mean generated by the pair f, g of continuous and strictly monotonic functions is the unique solution μ to the fixed point equation $$\mathcal{M}_{A_{(f)},A_{(g)}}(\mu )=\mu ,$$where A _(f) and A _(g) are the quasiarithmetic means respectively generated by f and g. In this article, the operator \({\mathcal{M}_{M,N}}\) is studied under less restrictive conditions and a general fixed point theorem is derived from an explicit formula for the iterates \({\mathcal{M} _{M,N}^{n}}\). The concept of class of generalized Cauchy means associated to a given family of mixing pairs of means is introduced and some distinguished families of pairs are presented. The question of equality in these classes of means remains a challenging open problem. Mathematics Subject Classification 26E60 47H10 Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (14) References1.Aczél J.: Lectures on Functional Equations and their Applications. Academic Press, New York (1966)MATH2.Berrone L.R.: Decreasing sequences of means appearing from non-decreasing functions. Publ. Math. Debrecen 55(1–2), 53–72 (1999)MathSciNetMATH3.Berrone L.: Invariance of the Cauchy mean value expression with an application to the problem of equality of Cauchy means. Internat. J. Math. Math. Sci. 2005(18), 2895–2912 (2005)MathSciNetCrossRefMATH4.Berrone L.R.: A dynamical characterization of quasilinear means. Aequationes Math. 84(1), 51–70 (2012)MathSciNetCrossRefMATH5.Berrone, L.R., Lombardi, A.L.: A note on equivalence of means. Publ. Math. Debrecen 58, Fasc. 1–2, 49-56 (2001)6.Berrone L.R., Moro J.: Lagrangian means. Aequationes Math. 55, 217–226 (1998)MathSciNetCrossRefMATH7.Berrone L.R., Moro J.: Cauchy means. Aequationes Math. 60, 1–14 (2000)MathSciNetCrossRefMATH8.Bullen P.S.: Handbook of Means and their Inequalities. Series Mathematics and its Applications. 2nd ed. Kluwer Academic Publisher, London (2003)CrossRefMATH9.Hardy G., Littlewood J.E., Pólya G.: Inequalities, 1st ed. Cambridge Univ. Press, Cambridge (1934)MATH10.Matkowski J.: Solution of a regularity problem in equality of Cauchy means. Publ. Math. Debrecen 64(3–4), 391–400 (2004)MathSciNetMATH11.Matkowski J.: Generalized weighted quasi-arithmetic means. Aequationes Math. 79, 203–212 (2010)MathSciNetCrossRefMATH12.Losonczi L.: Equality of two variable weighted means: reduction to differential equations. Aequationes Math. 58(3), 223–241 (1999)MathSciNetCrossRefMATH13.Losonczi L.: Equality of Cauchy means values. Publ. Math. Debrecen 57(1–2), 217–230 (2000)MathSciNetMATH14.Losonczi L.: Equality of two variable Cauchy mean values. Aequationes Math. 65(1–2), 61–81 (2003)MathSciNetMATH About this Article Title Generalized Cauchy means Journal Aequationes mathematicae Volume 90, Issue 2 , pp 307-328 Cover Date2016-04 DOI 10.1007/s00010-015-0341-7 Print ISSN 0001-9054 Online ISSN 1420-8903 Publisher Springer International Publishing Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Analysis Combinatorics Keywords 26E60 47H10 Industry Sectors Finance, Business & Banking Authors Lucio R. Berrone (1) Author Affiliations 1. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Laboratorio de Acústica y Electroacústica, Facultad de Cs. Exactas, Ing. y Agrim., Univ. Nac. de Rosario, Riobamba 245 bis, 2000, Rosario, Argentina Continue reading... To view the rest of this content please follow the download PDF link above.