Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces

TL;DR

This paper presents new reverse inequalities related to Schwarz, triangle, and Bessel inequalities in inner product spaces, leading to improved bounds and new Gruss type inequalities with applications to integral inequalities.

Contribution

It introduces novel reverse inequalities that enhance existing results and applies them to derive new Gruss type inequalities and integral inequality applications.

Findings

Improved bounds for Schwarz, triangle, and Bessel inequalities.

New Gruss type inequalities in inner product spaces.

Applications to integral inequalities.

Abstract

Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces that improve some earlier results are pointed out. They are applied to obtain new Gruss type inequalities in inner product spaces. Some natural applications for integral inequalities are also pointed out.