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Invariance of the Cauchy mean-value expression with an application to the problem of representation of Cauchy means

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  • Lucio R. Berrone

Abstract

The notion of invariance under transformations (changes of coordinates) of the Cauchy mean-value expression is introduced and then used in furnishing a suitable two-variable version of a result by L. Losonczi on equality of many-variable Cauchy means. An assessment of the methods used by Losonczi and Matkowski is made and an alternative way is proposed to solve the problem of representation of two-variable Cauchy means.

Suggested Citation

  • Lucio R. Berrone, 2005. "Invariance of the Cauchy mean-value expression with an application to the problem of representation of Cauchy means," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-18, January.
    • Handle: RePEc:hin:jijmms:534590
    DOI: 10.1155/IJMMS.2005.2895
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