Geometric Properties Of Generalized Orlicz Sequence Spaces

According to the needs of the different application, a variety of forms of Orliczspaces are promoted by many scholars. For example, modular sequence spaces,Musielak-Orlicz sequence spaces, Musielak-Orlicz function spaces and so on. Someproperties of Orlicz spaces are discussed, and the properties provide a basis and aconvenience for other research fields. This thesis mainly introduces a new modularfunction by use of Banach sequence norm, and a kind of generalized Orliczsequence space is gived. Moreover, Its some geometric properties are also obtained.First, criteria for extreme points of Orlicz sequence spaces equipped with theOrlicz norm and the Luxemburg norm are given respectively. It is proved that Orliczsequence spaces equipped with the Orlicz norm and the Luxemburg norm have theλ-property.Second, the monotonicity of the Orlicz sequence spaces equipped with theOrlicz norm and the Luxemburg norm are proved. when the space X satisfies someconditions, the generalized Orlicz sequence spaces equipped with the Orlicz normand the Luxemburg norm are strictly monotonous and uniformly monotonous.In the end, the values of monotonous coefficients of the generalized Orliczsequence spaces equipped with the Orlicz norm and the Luxemburg norm arediscussed.