On the H\"older and Cauchy--Schwarz inequalities

TL;DR

This paper explores a generalized form of the H"older inequality and examines its connections to an improved version of the Cauchy--Schwarz inequality, enhancing understanding of these fundamental mathematical tools.

Contribution

It introduces a generalized H"older inequality and discusses its relation to an improved Cauchy--Schwarz inequality, providing new insights into classical inequalities.

Findings

Established a generalized H"older inequality.

Connected the generalized inequality to an improved Cauchy--Schwarz inequality.

Enhanced understanding of the relationships between these inequalities.

Abstract

A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.