H-Points and H-Property of the Orlicz Spaces Endowed With the s-Norms

Abstract

In this paper, we investigate the set of H-points on the unit sphere of the Orlicz spaces over non-atomic and purely atomic measure spaces. Building upon these arguments, we establish a criteria for the H-property in Orlicz spaces. In addition, our results yield several consequences related to the geometric properties of the Orlicz spaces, particularly concerning extreme points, strongly extreme points, strictly convex, midpoint locally uniformly convex, denting points and G-property. This study unifies and extends previous results obtained for the Orlicz and Luxemburg norms and fills a gap in the literature concerning the $p$-Amemiya norms.