Reverses of the Schwarz Inequality in Inner Product Spaces Generalising a Klamkin-McLenaghan Result

TL;DR

This paper introduces new reverse inequalities for the Schwarz inequality in inner product spaces, extending classical results and providing applications to Lebesgue integrals, thus broadening the theoretical understanding and practical utility of these inequalities.

Contribution

It generalizes the Klamkin-McLenaghan result to new reverse inequalities in inner product spaces and applies these findings to Lebesgue integrals.

Findings

New reverse Schwarz inequalities established.

Extensions of classical inequalities to positive n-tuples.

Applications demonstrated in Lebesgue integral context.

Abstract

New reverses of the Schwarz inequality in inner product spaces that incorporate the classical Klamkin-McLenaghan result for the case of positive n-tuples are given. Applications for Lebesgue integrals are also provided.