# Inequalities that sharpen the triangle inequality for sums of $N$ functions in $L^p$

## TL;DR

This paper investigates inequalities in $L^p$ spaces that strengthen the classical triangle inequality when summing multiple functions, providing refined bounds and insights.

## Contribution

It introduces new inequalities that sharpen the triangle inequality for sums of multiple functions in $L^p$, extending existing results.

## Key findings

- Derived sharper $L^p$ inequalities for sums of $N$ functions
- Extended classical triangle inequality with new bounds
- Provided theoretical framework for improved $L^p$ estimates

## Abstract

We study $L^p$ inequalities that sharpen the triangle inequality for sums of $N$ functions in $L^p$.