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

Lucio R. Berrone
2005 International Journal of Mathematics and Mathematical Sciences  
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.
doi:10.1155/ijmms.2005.2895 fatcat:rtpm5t4g3zb37izlq6c2n7emmu