Comparison of differences between arithmetic and geometric means

Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means

Concentration of the Ratio between the Geometric and Arithmetic Means

This paper is motivated by the article [GluMi] by E. Gluskin and V. Milman, who considered the variant ∏n i=1 |yi| ≤ √ n−1 ∑n i=1 y 2 i of the AM-GM inequality in the equal weights case. Roughly speaking, they showed that the ratio ∏n i=1 |yi|/ √ n−1 ∑n i=1 y 2 i is bounded below by 0.394 asymptotically in n and with high probability, where probability refers to Haar measure on the euclidean un...

An Inequality between Compositions of Weighted Arithmetic and Geometric Means

Let P denote the collection of positive sequences defined on N. Fix w ∈ P. Let s, t, respectively, be the sequences of partial sums of the infinite series ∑ wk and ∑ sk, respectively. Given x ∈ P, define the sequences A(x) and G(x) of weighted arithmetic and geometric means of x by An(x) = n ∑ k=1 wk sn xk, Gn(x) = n ∏ k=1 x wk/sn k , n = 1, 2, . . . Under the assumption that log t is concave, ...

A Refinement of the Inequality between Arithmetic and Geometric Means

In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement. (1) exp 2 1 − n i=1 α i x

On Second Geometric-Arithmetic Index of Graphs

The concept of geometric-arithmetic indices (GA) was put forward in chemical graph theory very recently. In spite of this, several works have already appeared dealing with these indices. In this paper we present lower and upper bounds on the second geometric-arithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish Nordhaus-Gaddum-type results for GA2.