Banach空间中一类新的几何常数  

A New Class of Geometric Constants in Banach Spaces

作　　者：张海霞[1] 崔欢欢[2] 李浩[1] 

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007 [2]洛阳师范学院数学科学学院,河南洛阳471022

出　　处：《河南科技大学学报（自然科学版）》2014年第1期79-82,7,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11126284);河南省基础与前沿技术研究计划项目(102300410012)

摘　　要：对Banach空间的一致非方性质进行了刻画,引入一类几何常数H(X)和h(X)并得到常数H(X)和凸性模δX(ε)的关系等式,且证明了Banach空间一致非方的充分必要条件是H(X)不超过2。另外,计算了一些具体Banach空间上常数H(X)和h(X)的精确值。The uniform nonquareness of a Banach space was characterized in this paper. Two new geometric constants H( X) and h( X) were introduced. And the relation equation between H( X) and the modulus of convexity δX( ε) was obtained. It is also proved that a Banach space is uniformly nonsquare if and only if the value of H( X) is less than 2. The exact values of H( X) and h( X) for some concrete Banach spaces are computed.

关 键 词：BANACH空间 调和平均 一致非方 

分 类 号：O177.2[理学—数学]