Some Geometric Constants And Applications In Orlicz Space

As an important part of Banach space theory,Orlicz space geometry theory is widely used.In particular,it is particularly prominent in the application of fixed point theory.Using geometric constants to research the geometric properties of Orlicz space is a way that mathematical workers have been practicing and exploring since a long time ago.At the same time,they also expanded the new research direction and made its application more extensive by giving different norms to Orlicz spaces.The study of Orlicz spaces with different norms can make the application of geometric constants more general,and can also obtain different results to enrich the properties of fixed points in these Orlicz spaces.The full text is split into four parts to calculate the M-constant of Orlicz space,García-Falset coefficient and Domínguez-Benavides coefficient of Orlicz sequence space respectively.The main contents are as follows:Firstly,this part describes the purpose and significance of studying geometric theory and geometric constants of Banach spaces,and introduces the basic structure of Orlicz spaces with Luxemburg norm,Orlicz norm and s norm,as well as the main content of fixed point theory.Secondly,the M-constant is one of several geometric constants in space,which has a wide range of applications.Sims studied the M-constant and concluded that it is closely related to the property of fixed points.In this chapter,we study the concrete expression of M-constant in Orlicz space with Luxemburg norm and the sufficient condition of weak fixed point property of subspace E(37).Thirdly,in order to obtain García-Falset coefficient in the Orlicz sequence space with s-norms,in chapter 3,we first give the necessary and sufficient conditions for sl(37),to have the Schur property.Using this condition,García-Falset coefficient is given.On this basis,we give the equivalent condition that Orlicz sequence space with s-norms has weak fixed point property.Finally,based on the study of García-Falset coefficients in the previous chapter,the Domínguez-Benavides coefficients of Orlicz sequence spaces with s-norms are given.On this basis,the equivalent condition of fixed point property in Orlicz sequence space with s-norms is solved.