New Geometric Constant Related to the P-angle Function in Banach Spaces

TL;DR

This paper introduces a new geometric constant based on the P-angle function in Banach spaces, exploring its properties and implications for geometric characteristics like convexity and fixed point properties.

Contribution

It defines a novel angular geometric constant linked to the P-angle function and investigates its properties and connections to key geometric features of Banach spaces.

Findings

Established inequalities involving the new constant and existing geometric constants.

Linked the new constant to uniform non-squareness and convexity conditions.

Provided criteria for fixed point properties based on the new constant.

Abstract

In this paper, combined with the P-angle function of Banach spaces and the geometric constants that can characterize Hilbert spaces, the new angular geometric constant is defined. Firstly, this paper explores the basic properties of the new constant and obtains some inequalities with significant geometric constants. Then according to the derived inequalities, this paper studies the relationship between the new constant and the geometric properties of Banach spaces. Furthermore, the necessary and sufficient condition for uniform non-squareness, and the sufficient conditions for uniform convexity, the normal structure and the fixed point property will be established.