engleski

On the logarithmic mean in n variables

The logarithmic mean, defined for two positive real numbers by L(x, y)= (y - x)/(ln y - ln x), for x \neq y ; L(x, x)= x ; doesn't give insights about possible generalizations to several variables. However, if we write this mean in integral form, we get the idea for generalization using the standard notion of Euclidean simplex. In this talk we consider two such generalizations given by A.O. Pittenger and E. Neuman. We also show some other ideas for generalizing the logarithmic mean on $n$ variables using some different methods, and we show that these methods bring us again to the main two generalizations of Pittenger and Neuman. At the end we also mention some further generalizations of such means.

logarithmic mean; Euclidean simplex

nije evidentirano