A family of weighted Erd\H{o}s-Mordell inequality and applications

TL;DR

This paper introduces weighted generalizations of the Erd ext{"o}s-Mordell inequality, strengthening the original inequality and extending its applicability through new variations and weighted versions.

Contribution

The paper presents novel weighted generalizations of the Erd ext{"o}s-Mordell inequality, including strengthened and varied forms, expanding its theoretical framework.

Findings

Derived strengthened versions of Erd ext{"o}s-Mordell inequality.

Established weighted generalizations applicable to new variations.

Extended the inequality's scope through multiple generalizations.

Abstract

We establish some new generalizations of Erd\H{o}s-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erd\H{o}s-Mordell inequality. We also found two other variations of Erd\H{o}s-Mordell inequality to be generalizable in the same way.