A number ’a’ is between two numbers x andy if and only ifa is a convex combination of x andy, in other words, it is a "weighted mean" of x andy. 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… Expand

In a very interesting and recent note, Tung-Po Lin [I] obtained the least value q and the greatest value p such that M <L<M P q is valid for all distinct positive numbers x and y where M (x +.y.)s… Expand

The logarithmic mean is generalized for n positive arguments x1, . . . , xn by examining series expansions of typical mean numbers in case n = 2. The generalized logarithmic mean defined as a series… Expand

The inequality between the arithmetic mean (AM) and geometric mean (GM) of two positive numbers is well known. This article introduces the logarithmic mean, shows how it leads to refinements of the… Expand

The fact that the logarithmic mean of two positive numbers is a mean, that is, that it lies between those two numbers, is shown to have a number of consequences.

The ordinary Binomial Theorem states that for any nonnegative integer n, (1 + x) n = n k=0 n k x k = ∞ k=0 n k x k , where n k = n(n − 1) · · · (n − k + 1) k! if k ≥ 1; n 0 = 1 ;… Expand

An integral representation of Neuman is extended and used to suggest a multidimensional weighted generalized logarithmic mean. Some inequalities are established for such means. A number of known… Expand