Paper Title:

Scope of the Logarithmic Mean

Author(s):

Murali Rao and Agnish Dey

Department of Mathematics,
University of Florida,
1400 Stadium Road, Gainesville,
Florida 32611,
U. S. A.

E-mail: mrao@ufl.edu

URL: http://people.clas.ufl.edu/mrao

E-mail: agnish@ufl.edu

URL: http://people.clas.ufl.edu/agnish 

Abstract:

A number a is between two numbers x and y if and only if a is a convex combination of x and y, in other words, it is a "weighted mean" of x and y. Geometric mean, arithmetic mean are well known examples of these "means". Of more recent vintage is the logarithmic mean which has been considered in many articles in the literature. In this note, we first discuss some of its properties. Then we shall introduce the L function and explore the inverse of this function and its connection with the Lambert's Omega function.

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