The Exposed Points, Uniformly Noncreasy And The Smoothness In Generalized Orlicz Spaces

The exposed points and strongly exposed points are basic notions in the geometric theory of Banach spaces. The exposed points are always characterized the strict convexity of normed spaces, and the strongly exposed points are the link between Radon-Nikodym property and the geometric structure. Moreover, Musielak-Orlicz spaces are the ideal frame for studying the elasticity.In this thesis, we study the exposed points and strongly exposed points in Musielak-Orlicz spaces, uniformly noncreasy in Orlicz-Bochner spaces and smooth-ness in Orlicz spaces.Firstly, we investigate exposed points and strongly exposed points of Musielak-Orlicz sequence spaces endowed with Orlicz norm and Luxemburg norm, respectively. And we give the sufficient and necessary conditions of exposed points and strongly exposed points, respectively.Secondly, we discuss noncreasy and uniformly noncreasy in Orlicz-Bochner function spaces. And we obtain that they are noncreasy (uniformly noncreasy) if and only if they are strictly convex (uniformly convex) or smooth (uniformly smooth).Lastly, we investigate U property in any finite dimensional subspace of clas-sical Orlicz space. And we obtain that any finite dimensional subspace of classical Orlicz space has U property if and only if its any nonzero element is smooth point.