Uniformly non-ln(1), locally uniformly non-ln(1) and non-ln(1) properties in Orlicz-Bochner function spaces endowed with the Orlicz norm

Some criteria are given in this paper for uniformly non-ln(1), locally uniformly non-ln(1) and non-ln(1) properties of Orlicz-Bochner function spaces endowed with the Orlicz norm. As the consequence, we can immediately get the characterization of B-convexity, uniform nonsquareness, local uniform nonsquareness and nonsquareness in Orlicz-Bochner function spaces, although some of them were obtained in recent years.