Banach空间中几种凸性的研究

发布时间：2018-05-06 11:13

本文选题：Banach空间 + ω-非常极凸　；参考：《广西师范学院》2017年硕士论文

【摘要】：Banach空间中的凸分析理论有着极其精妙的性质和作用,这些凸分析的理论推动着Banach空间几何理论的快速和深层次的发展.到目前为止,Banach空间中的凸性研究已有了极大的进步并且相对完善,但对一些已知的凸性的推广以及更深层次讨论还不是很完善.本文定义了ω-非常极凸空间、局部一致极凸空间、平均一致极凸空间以及k-极凸空间,研究了它们的性质、特征及与其它凸性之间的关系,得到了一些较好的结果,从而推广了一致极凸空间和强极凸空间,本文由以下五章组成.第一章:预备知识.第二章:本章引入ω-非常极凸空间,证明了它弱于ω--drop凸空间强于弱非常凸空间的一类空间,并给出了它的一些简单性质.第三章:本章本文用一种新的手法对K-极凸空间重新进行了刻画,并进一步证明了其与何仁义在文[24]中K-极凸及魏文展在[6]中刻画的K-DC等价.第四章:在一致极凸和一致极光滑的概念的基础上,定义了局部一致极凸空间和局部一致极光滑空间.第五章:在一致极凸和一致极光滑的概念的基础上,定义了平均一致极凸空间和平均一致极光滑空间.
[Abstract]:Convexity analysis theory in Banach space has very subtle properties and functions. These convex analysis theories promote the rapid and deep development of geometric theory in Banach space. Up to now, the research on convexity in Banach spaces has been greatly improved and relatively perfect, but the generalization of some known convexity and further discussion are not very perfect. In this paper, we define 蠅 -very convex space, locally uniformly extremely convex space, average uniformly extremely convex space and k-extremely convex space. We study their properties, characteristics and relations with other convexities. Some good results are obtained. Thus we generalize the uniformly extremely convex space and the strongly extremely convex space. This paper is composed of the following five chapters. Chapter one: preparatory knowledge. Chapter 2: in this chapter, we introduce 蠅 -very very convex space, and prove that it is weaker than 蠅 -drop convex space than a class of weakly very convex space, and give some simple properties of it. Chapter 3: in this chapter, we recharacterize K-extremely convex space with a new technique, and further prove that it is equivalent to the K-DC of K- extreme convexity in [24] and that of Wei Wenzhan in [6]. Chapter 4: based on the concepts of uniform extreme convexity and uniform extreme smoothness, locally uniformly extremely convex spaces and locally uniformly extremely smooth spaces are defined. Chapter 5: on the basis of the concepts of uniform extreme convexity and uniform extreme smoothness, the average uniformly extremely convex space and the average uniformly extremely smooth space are defined.
【学位授予单位】：广西师范学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177.2

【参考文献】