Some Geometry Properties Of The Musielak-Orlicz Function Space

According to the requirement of various subjects and applications, there are many generalizations of Orlicz spaces. Musielak-Orlicz spaces are common generalization.In this paper, we mainly investigate some properties of Musielak-Orlicz spaces. It consists of three parts. The main results of this paper are summarized as following :First it reviewed that a survey of the theory of Orlicz and Musielak-Orlicz spaces, and it evaluated and summarized the pioneers'main research results and showing the background and significance of the content of each part in this paper.As we known that, extreme point takes part in important role of some banches in math. In chapter 2, we give the criteria of extreme point in Musielak-Orlicz function space. Meanwhile we get necessity and sufficient condition for that Musielak-Orlicz function space are rotundity as corollaries.H property is an magnificent concept in Banach space. H point is the meticulous and pointwise description of the H property. In chapter 3, we present the criteria of H-point in Musielak-Orlicz function space.The roughness norm descriptes some non-Frechet derivative indeed. It is stronger than pointwise rough and weaker than the strong rough in roughness. Its concept is between nowhere Frechet derivative and uniformly non-Frechet derivative in derivative.At last, by the criteria of ronghness in Orlicz space, the criteria of the roughness in Musielak-Orlicz function space are obtained. It includes piontwise rough, the strong rough and the rough and so on. Futhermore it talks about the relationship between the roughness and the derivative in Musielak-Orlicz function space equipped with the Luxuember norm and Orlicz norm respectively as well. Making use of the criteria of the extreme point in Musielak-Orlicz...