Analog of modulus of convexity for Grand Lebesgue Spaces

TL;DR

This paper introduces a new measure called the characteristic of convexity for Grand Lebesgue Spaces, providing an analog to the classical modulus of convexity, to analyze their geometric properties.

Contribution

It defines and evaluates the degree of convexity for GLS, extending classical convexity concepts to these function spaces.

Findings

Defined the characteristic of convexity (COC) for GLS

Established properties of COC in relation to GLS

Provided insights into the geometric structure of GLS

Abstract

We introduce and evaluate the degree of convexity of an unit ball, so-called, characteristic of convexity (COC) for the Grand Lebesgue Spaces, (GLS), which is a slight analog of the classical notion of the modulus of convexity (MOC).