New geometric constants of isosceles orthogonal type
Functional Analysis
2022-03-11 v2
Abstract
Based on the parallelogram law and isosceles orthogonality, we define a new orthogonal geometric constant. We first discuss some basic properties of this new constant. Next, we consider the relation between the constant and the uniformly non-square property. Moreover, a generalized constant is also introduced and some basic properties are presented. It is shown that, for a normed space, the constant value is equal to 1 if and only if the norm can be induced by the inner product. Finally, we verify that this constant is closely related to the well-known geometric constants through some inequalities.
Keywords
Cite
@article{arxiv.2111.08392,
title = {New geometric constants of isosceles orthogonal type},
author = {Qi Liu and Zhijian Yang and Yongjin Li},
journal= {arXiv preprint arXiv:2111.08392},
year = {2022}
}