The Proof of Alzer's Conjecture on Generalized Logarithmic Mean

TL;DR

This paper proves Alzer's conjecture on generalized logarithmic mean by first confirming Lou's related conjecture on inverse harmonic mean, resolving a long-standing mathematical question.

Contribution

The paper introduces a proof of Alzer's conjecture by establishing Lou's conjecture, advancing the understanding of generalized means.

Findings

Proof of Lou's conjecture on inverse harmonic mean

Resolution of Alzer's conjecture on generalized logarithmic mean

Enhanced understanding of relationships among generalized means

Abstract

In 1987, Alzer posed a conjecture on generalized logarithmic mean, which was introduced by Stolarsky in 1975. To prove Alzer's conjecture, Lou posed a conjecture on generalized inverse harmonic mean in 1995. By proving Lou's conjecture, the paper yields Alzer's conjecture finally.