Geometric constants for quantifying the difference between orthogonality types

TL;DR

This paper introduces new geometric constants to measure differences between Roberts and Birkhoff orthogonality in normed planes, using characterizations via bisectors and linear transformations.

Contribution

It provides novel geometric constants and characterizations that quantify the difference between two types of orthogonality in normed planes.

Findings

Defined new geometric constants for orthogonality comparison

Characterized Roberts orthogonality via bisectors and linear transformations

Quantified differences between orthogonality types

Abstract

This paper is devoted to introduce new geometric constants that quantify the difference between Roberts orthogonality and Birkhoff orthogonality in normed planes. We start by characterizing Roberts orthogonality in two different ways: via bisectors of two points and using certain linear transformations. Each of these characterizations yields one of those geometric constants that we will study.