Non-squareness and local uniform non-squareness properties of Orlicz-Lorentz function spaces endowed with the Orlicz norm

TL;DR

This paper establishes the necessary and sufficient conditions under which Orlicz-Lorentz function spaces with the Orlicz norm exhibit non-squareness and local uniform non-squareness properties.

Contribution

It provides a complete characterization of non-squareness properties in Orlicz-Lorentz spaces with the Orlicz norm, advancing the understanding of their geometric structure.

Findings

Characterization of non-squareness conditions

Conditions for local uniform non-squareness

Enhanced understanding of geometric properties

Abstract

In this paper the necessary and sufficient conditions were given for Orlicz-Lorentz function space endowed with the Orlicz norm having non-squareness and local uniform non-squareness.