On the equivalent p-th von Neumann-Jordan constant associated with isosceles orthogonality in Banach spaces

TL;DR

This paper introduces a new geometric constant in Banach spaces based on isosceles orthogonality, linking it to the p-th von Neumann-Jordan constant and exploring its properties and geometric implications.

Contribution

It defines a novel constant related to isosceles orthogonality, analyzes its bounds, and connects it to key geometric properties of Banach spaces.

Findings

The constant's basic properties are established.

Upper and lower bounds of the constant are calculated.

The upper bound is shown to be attainable in examples.

Abstract

In this paper, we define a new geometric constant based on isosceles orthogonality, denoted by . Through research, we find that this constant is the equivalent p-th von Neumann Jordan constant in the sense of isosceles orthogonality. First, we obtain some basic properties of the constant. Then, we calculate the upper and lower bounds of the constant. Through three examples, it is found that the upper bound of the constant is attainable. We also compare the relationship between this constant and other constants. Finally, we establish the connection between the constant and some geometric properties in Banach spaces, such as uniform non-squareness, uniform smoothness.