本文選題：Banach空間 + ω-非常極凸��； 參考：《廣西師范學院》2017年碩士論文

【摘要】：Banach空間中的凸分析理論有著極其精妙的性質(zhì)和作用,這些凸分析的理論推動著Banach空間幾何理論的快速和深層次的發(fā)展.到目前為止,Banach空間中的凸性研究已有了極大的進步并且相對完善,但對一些已知的凸性的推廣以及更深層次討論還不是很完善.本文定義了ω-非常極凸空間、局部一致極凸空間、平均一致極凸空間以及k-極凸空間,研究了它們的性質(zhì)、特征及與其它凸性之間的關系,得到了一些較好的結(jié)果,從而推廣了一致極凸空間和強極凸空間,本文由以下五章組成.第一章:預備知識.第二章:本章引入ω-非常極凸空間,證明了它弱于ω--drop凸空間強于弱非常凸空間的一類空間,并給出了它的一些簡單性質(zhì).第三章:本章本文用一種新的手法對K-極凸空間重新進行了刻畫,并進一步證明了其與何仁義在文[24]中K-極凸及魏文展在[6]中刻畫的K-DC等價.第四章:在一致極凸和一致極光滑的概念的基礎上,定義了局部一致極凸空間和局部一致極光滑空間.第五章:在一致極凸和一致極光滑的概念的基礎上,定義了平均一致極凸空間和平均一致極光滑空間.
[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.
【學位授予單位】：廣西師范學院
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O177.2

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本文編號：1852090