I-Convexity?Q-Convexity And Non-l_n¹ Property In Orlicz-Bochner Spaces

Orlicz-Bochner spaces provide a more reasonably theoretical framework for the research of differential equations,vector measure and other problems.Moreover,I-convexity Q-convexity,non-ln(1)property play important roles in fixed point theory and any other fields.In this paper the characteristics of these geometric properties are investigated in Orlicz-Bochner space,and the details are as follows:Firstly,some criteria for Orlicz-Bochner function spaces and sequence spaces be-ing I-convex are obtained,which generalize some relevant results in Lebesgue-Bochner spaces.Secondly,we get some criteria for Orlicz-Bochner function spaces and sequence spaces being Q-convex.Thirdly,some criteria are given for Orlicz-Bochner sequence spaces and Orlicz-Bochner function spaces endowed with the Orlicz norm being non-ln(1)and locally uniformly non-ln(1),which generalize some results of nonsquareness and locally uniform nonsquareness.