Some Properties Of JAMES Type Constant And Von Neumann-Jordan Type Constant

James type constant JX,t(τ) and von Neumann-Jordan type constant Ct(X) are gen-eralizations of James constant and von Neumann-Jordan constant respectively. They arealso two unified approaches for two type constants. This paper mainly studies some prop-erties of James type constant and von Neumann-Jordan constant. We also study severalconcrete conditions of some special spaces. We will seperate the paper into three parts todemonstrate according to the content.In chapter one, we mainly introduce the background and the current situation of thispaper. We also introduce some basic definitions and results of this paper.In chapter two, we mainly introduce James type constant. Firstly, we study somenew properties of James type constant on the basis of the current situation. For example,monotonicity, continuous, uniform non-squareness , and so on. Secondly, this chapter alsoinvestigates some relations between James type constants when the coe*cient of t take dif-ferent value. In addition, we also study the relation between JX,t(τ) and JX*,t(τ). Finally,we calculate James constants for three concrete spaces which consist of lp space, l∞* l1space, and Xλ,p space. The three examples are the main conclusions of this dissertation.In chapter three, we mainly introduce von Neumann-Jordan type constant. Firstly,we study some new properties of von Neumann-Jordan such as its equivalent form, equiva-lent conditions of uniformly non-square which are described by von Neumann-Jordan typeconstant, the relation between JX,t(τ) and JX*,t(τ), and so on. Secondly, we introduce some su*cient conditions for normal structure and uniformly normal structure which arecharacterized by von Neumann-Jordan type constant. These results furthur improve someprevious results. Finally, we give some relations among several constants, such as C1′(X)and C1(X), C1(X*) and C1(X), and so on.