On modulus of noncompact convexity for a strictly minimalizable measure of noncompactness

TL;DR

This paper investigates the properties and continuity of the modulus of noncompact convexity linked to a strictly minimalizable measure of noncompactness, enhancing understanding of its behavior in Banach spaces.

Contribution

It introduces and analyzes the modulus of noncompact convexity for a specific measure of noncompactness, establishing its properties and continuity.

Findings

The modulus of noncompact convexity has specific mathematical properties.

It is continuous on the interval [0, Φ(closure of B_X)].

The paper provides foundational insights into measures of noncompactness.

Abstract

In this paper we consider modulus of noncompact convexity $\Delta_{X,\varPhi}$ associated with the strictly minimalizable measure of noncompactness $\varPhi$. We also give some its properties and show its continuity on the interval $[0,\varPhi(\bar{B}_X))$.