Some Point-wise Properties In Musielak-orlicz Space

According to the development of various theories and applications, different kinds of generalizations of Orlicz space are introduced, and the class of Musielak-Orlicz space is a well known generalization of this type. A point-wise geometric property is actually point-wise and refined characterization of the corresponding property of the underlying space. The introduction of point-wise method is a revolutionary development of Orlicz space. In this thesis, some point-wise geometric properties of Musielak-Orlicz space are studied.Thesis is organized by three parts as follows:Firstly, the developments of Orlicz space and Musielak-Orlicz space are introduced and the main existing research results are summarized. Moreover, background and significance of the research in this thesis are presented.Secondly, as well known, exposed point and w * strongly exposed point are two basic concepts in the geometric theory of Banach space, have a lot of applications in control theory and the theory of approximation, and have remarkable geometric significance. H. Hudzik and Yunan Cui showed that weakly strongly exposed and very smooth is a pair of properties dual to each other. This illustrated further the significance of exposed property. In this part, a criterion of w * strongly exposed point in Musielak-Orlicz sequence space is presented.Finally, some sufficient and necessary conditions of exposed point and w *strongly exposed point respectively, are shown.