Convexity And Normal Structure Of Orlicz-Bochner Spaces

Orlicz-Bochner spaces provide a more scientific theoretical framework for the study of 'equations and other problems.Moreover,P-convexity(F-convexity),O-convexity(E-convexity),normal structure and uniformly non-ln(1)(B-convexity)play an important role in fixed point theory and any other fields.In this thesis,we study these properties in Orlicz-Bochner spaces and mainly get the results as follows.Firstly,we get the criteria for P-convexity and F-convexity in Orlicz-Bochner sequence spaces endowed with the Orlicz norm.Secondly,Criteria for O-convexity and E-convexity were obtained in Orlicz-Bochner spaces,including the function spaces endowed with the Orlicz norm or the Luxemburg norm,and the sequence spaces endowed with the Orlicz norm or the Luxemburg norm.Moreover,a sufficient condition was got for Orlicz-Bochner spaces having the fixed point property.Thirdly,we investigated the characteristics of Orlicz-Bochner function spaces with the normal structure under some condition.Which generalize the related result in the Lebesgue-Bochner function spaces.Finally,Criteria for the uniformly non-lnln(1)and B-convexity in Orlicz-Bochner spaces were obtained.Which generalize some results about the uniformly nonsquare property.