International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 18, Pages 2895-2912
doi:10.1155/IJMMS.2005.2895
Invariance of the Cauchy mean-value expression with an application to the problem of representation of Cauchy means
Lucio R. Berrone
Consejo Nacional de Investigaciones Científicas y Técnicas, Departamento de Matemática, Facultad de Ciencias Exactas, Ingenieria y Agrimensura, Universidad Nacional de Rosario, Avenue Pellegrini 250, Rosario 2000, Argentina
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.