%0 Journal Article
%T On the comparison of Cauchy mean values
%A Losonczi L¨˘szl¨®
%J Journal of Inequalities and Applications
%D 2002
%I Springer
%X Suppose that and exist, with , on . Then there is (moreover if ) such that where denotes the divided difference of at the points . This is the Cauchy Mean Value Theorem for divided differences (see e.g. [4]). If the function is invertible then is a mean value of . It is called the Cauchy mean of the numbers and will be denoted by ). Here we completely solve the comparison problem of Cauchy means in the special cases and . In the general case we find necessary conditions (which are not sufficient) and also sufficient conditions (which are not necessary).
%K Divided differences
%K Cauchy mean value
%K Comparison of means
%K Gini mean
%U http://www.journalofinequalitiesandapplications.com/content/7/876016