Some Properties Of Three Geometry Constants Of Banach Space

In this paper, we mainly study some constants of Banas-Frsaczieck space and l1-l2space. For example James constant, von Neumann-Jordan constant, Zbaganu constant and so on. And we also base on James type constant Jx,t(Υ) to define a generalized James type constant JX,t(p)(Υ), so we draw some conclusions. The paper is organized as follows:In part one, we chiefly introduce the background and the current situation of the modulus, James type constant and von Neumann-Jordan constant in Banach space. We also introduce the basic definitions, results related to geometric theories of a Banach space.In part two, this part is separated into four small sections to introduce.· For Banas-Frsaczieck space. We prove the value of moduli of convexity under specific conditions, James constant J(X)=-2λ/1+λ2; VonNeumann-Jordan constant CNJ(X)=C’NJ(X)=2-1/λ2under λ>√2; The value of generalized James type constant Jx,t(Υ) under specific conditions and the estimated value under certain conditions.· The value Cz(X)=(?)2is obtained for two-dimensional Day-James space l1-l2.· Another important inequality is deduced according to the relationship between the generalized James type constant and modulus of smoothness.· Similar to generalized James type constant Jx,t(Υ), we introduce a new generalized James type constant JX,t(p)(t) with a parameter p, which is generalized by JX,t(Υ).We base on it to receive the relationship with JX,t(p)(Υ) and Ρx(Υ).It also further improve and promote the other some conclusions of other authors.