# On Alzer's inequality

## TL;DR

This paper explores extensions and generalizations of Alzer's inequality, a Wirtinger-type inequality, and applies these results to derive sharp bounds for trapezoid inequalities and the geometric mean.

## Contribution

It introduces new extensions and generalizations of Alzer's inequality and applies them to obtain sharp bounds for related inequalities.

## Key findings

- New extensions of Alzer's inequality are proved.
- Sharp trapezoid type inequalities are derived.
- Precise bounds for the geometric mean are established.

## Abstract

Extensions and generalizations of Alzer's inequality; which is of Wirtinger type are proved. As applications, sharp trapezoid type inequality and sharp bound for the geometric mean are deduced.