New Inequalities and Applications

TL;DR

This paper introduces new inequalities, notably Theorem 2.1, which unify and extend existing inequalities like Nesbitt's, offering a simple, versatile tool with broad applications in mathematical inequality problems.

Contribution

The paper presents a new inequality in Theorem 2.1 that unifies and generalizes existing inequalities, including Nesbitt's, and provides a straightforward method for deriving numerous new inequalities.

Findings

Theorem 2.1 provides a unifying inequality applicable to various problems.

The new inequality simplifies the derivation of known inequalities.

Many existing inequalities can be obtained directly using the proposed inequality.

Abstract

This paper presents some new inequalities, the most important of which is the inequality given in Theorem 2.1. It can solve a class of inequalities by a unified method. An important application of the inequality given in Theorem 2.1 is to derive another new general form of inequality. The famous Nesbitt's inequality is a special case of this general form of inequality when n = 3. The new inequality in Theorem 2.1 proposed in this paper is easy to use and expand, and many new inequalities can be derived and obtained by direct calculation, so it has a wide range of applications. Many known inequalities can also be directly calculated by the inequalities proposed in this paper, and the calculation is simple and convenient.