On inequalities for convex functions

TL;DR

This paper explores properties of convex functions to derive new inequalities among real numbers and improves the reverse triangle inequality for aligned points in normed spaces.

Contribution

It introduces novel inequalities based on convex function properties and enhances the reverse triangle inequality in specific geometric configurations.

Findings

Derived new inequalities among real numbers using convex functions.

Provided an improved reverse triangle inequality for three aligned points.

Extended inequalities to normed space geometries.

Abstract

We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the particular case where three aligned points are considered in a normed space.