Monotocities In Orlicz Spaces Equipped With S-Norm

Functional analysis is basic tool in the research of modern mathematics,and it is applied in each subject of mathematics.Banach space is an important branch of functional analysis.As a special kind of Banach space,Orlicz spaces have great significance.Using the properties of generated function,the Orlicz spaces have a lot of different properties,and Orlicz spaces can provide sufficient references and examples for the study theory of abstract Banach spaces.Orlicz spaces provide new research ideas and proof techniques for solving geometric properties in Banach spaces.So far,the research on geometric proeprties in Orlicz spaces equipped with the Orlicz norm or the Luxemburg norm is almost finished.In this paper,we will discuss some geometric properties of Orlicz spaces equipped with s-norm.The results will further promote the development of the theory of Orlicz spaces.The dissertation is divided into the following four parts:In the first part,the development of theory of Orlicz spaces is reviewed,and the research status on the theory of Orlicz spaces at home and abroad is described.In the second part,a new s-norm equivalent to s-Luxemburg norm is introduced namely.It is proved that the Orlicz function space equipped the s-norm is complete s-normed linear spaces.We obtain the condition that Orlicz space equipped with s-norm is strict monotonicityIn the third part,we study the local uniformly monotonicity of the Orlicz space with s-norm and the criterion of Orlicz spaces equipped with s-norm is local uniformly monotonicity is given.