Some Geometric Properties Of Musielak-Orlicz Spaces

Some geometric properties of Orlicz spaces equipped with Orlicz norm, Luxemburg norm and a common generalization Musielak-Orlicz sequence spaces are investigated in this thesis.Moreover,some geometric coefficients of Orlicz function spaces and Musielak-Orlicz sequence spaces are also studied. It consists of four parts:The main results of the thesis are summarized as following: Chapter 1 Introduction:It is reviewed that developing course of the theory and geometric theory of Orlicz spaces during more than 60 years studies . Moreover , it is evaluating and summarizing the pioneer's main research results,and showing the background and significance of the content of each part in this thesis. Chapter 2 Convergent sequence coefficient in measure of Orlicz space:The weakly convergent sequence coefficient (MCS(X)) are fundamental concepts in geometry of Banach space.In this paper, the author introduces a new definition namely the convergent sequence coefficient in measure of Banach function spaces ( MCS for short).It is proved that if K is an nonempty bounded closed convex subset of X and T : K →K is an nonexpansive mappings then T has a fixed point in K for every Orlicz function space X with MCS ( X ) > 1.We also give sufficient and necessary conditions for Orlicz function space X to have MCS ( X ) > 1. Chapter 3 The weak convergent sequence coefficient of the Musielak-Orlicz sequence space:Concerning the discussion on the weakly convergent sequence coefficient,a formula for the weak convergent sequence coefficient of the Musielak-Orlicz sequence space lφequipped with the Luxemburg norm is calculated.As a consequence of this result,the coefficient for Nakano spaces l ( pi) is found. Chapter 4 Weak topology in Musielak-Orlicz sequence spaces:According to the requirement of various theories and application , there are many generalizations of Orlicz space . Musielak-Orlicz space is a common generalization. The weak topology of Musielak-Orlicz sequence space is investigates , the conclusion that had been get in Orlicz space has been expanded.The result can be enlarged to Musielak-Orlicz sequence space too.