Novel constants based on the generalization of Von Neumann-Jordan constant

TL;DR

This paper introduces new geometric constants derived from generalizing the parallelogram law, explores their properties and relationships with existing constants, and examines their implications for the structure of specific spaces.

Contribution

It presents novel geometric constants based on the generalization of the Von Neumann-Jordan constant and analyzes their properties and applications.

Findings

New geometric constants introduced and characterized.

Relationships established with existing geometric constants.

Conditions for normal structure derived from these constants.

Abstract

We introduce a new geometric constant based on a generalization of the parallelogram law, and study its properties as well as some relationships with other well-known geometric constants. A sufficient condition for normal structure is presented. Next, we introduce a constant and calculate its value in a specific space. Furthermore, we introduce another new constant and investigate some of its basic properties.