(K-β) Points Of Orlicz Spaces

(β)Points is an important pointwise property in Banach spaces.It is closely related to uniformly convex points,compactly uniformly convex points and H points.So far,some achievements have been obtained on(β)points.In this paper,we generalize the concept of(β)points in Banach spaces,introduce the concept of(k-β)points,and investigate the characterization for(k-β)points in classical Orlicz spaces and Musielak-Orlicz spaces.The full dissertation is divided into three chapters.The main contents of these thesis are as follows.The first chapter is the introduction.Firstly,the purpose and significance of this thesis are introduced.Then,the developing history and researching status both at home and abroad of Orlicz spaces and Musielak-Orlicz spaces are elaborated in detail.Finally,the main research contents of this thesis are introduced.The second chapter is the(k-β)points of Orlicz spaces.In this chapter,we first introduce the definition of(k-β)points in Banach space,and then discuss the characterizations for(k-β)points in Orlicz sequence spaces equipped with the Orlicz norm and Orlicz function spaces equipped with the Luxemburg norm,and the equivalent conditions for these spaces mentioned above to have local property(k-β)are given as corollaries.The three chapter is the(k-β)points of Musielak-Orlicz sequence spaces.In this chapter,we give the criterion for(k-β)points in Musielak-Orlicz sequence spaces equipped with the Orlicz norm,and basing on this criterion,we provide the necessary and sufficient conditions for these spaces to have local property(k-β).Then in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm we give a sufficient condition that a point on the sphere is a(k-β)points.