Research On A Related Contant To Uniform Nonsquareness

Since the 1960s, Banach space theory has made rapid development, especially the research on the geometric properties of space has made a lot of very good results. This paper will study the non-square space and its related geometric constant.First, this paper survey the development and some results of generalized orthogonality types, and give a outline for geometric constants and pointwise geometric constants of Banach space. These contents are helpful for the discussions in the rest of the paper.This paper further study generalized nonsquare constant A( X, r) introduced by Ji Donghai and Qiao Wenjing. It is proved that a normed linear space X is not strictly convex if and only if ?r∈(0 ,2),x , y∈SX, such that ; a Minkowski space X is not strictly convex if and only if ; a Banach space X is uniformly convex if and only if there does not exist r∈(0 ,2) such that A( X, r) =2. Exact values of A( X, r) for some classical Banach spaces are obtained.