A Generalisation of the Cassels and Greub-Reinboldt Inequalities in Inner Product Spaces

TL;DR

This paper generalizes classical inequalities in inner product spaces and explores their applications in various mathematical contexts such as integrals and sequences.

Contribution

It introduces a broad generalization of the Cassels and Greub-Reinboldt inequalities applicable to complex and real inner product spaces.

Findings

Extended inequalities to complex and real inner product spaces

Applied generalized inequalities to isotonic linear functionals, integrals, and sequences

Provided new bounds and relations in inner product space theory

Abstract

A generalisation of the Cassels and Greub-Reinboldt inequalities in complex or real inner product spaces and applications for isotonic linear functionals, integrals and sequences are provided.