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

摘要

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.