Strengthened Cauchy-Schwarz and H\"older inequalities

TL;DR

This paper introduces new identities in complex inner product spaces to provide a novel proof of strengthened Cauchy-Schwarz inequalities and extends these results to strengthened H"older inequalities.

Contribution

It offers new identities and a fresh proof for strengthened inequalities, and generalizes these results to H"older inequalities in complex inner product spaces.

Findings

New identities related to Cauchy-Schwarz in complex spaces

A novel proof of strengthened Cauchy-Schwarz inequalities

Extension to strengthened H"older inequalities

Abstract

We present some identities related to the Cauchy-Schwarz inequality in complex inner product spaces. A new proof of the basic result on the subject of Strengthened Cauchy-Schwarz inequalities is derived using these identities. Also, an analogous version of this result is given for Strengthened H\"older inequalities.