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Normal structure

机译:正常结构

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摘要

The difinition of normal structure was introduced by Brodskii and Milman, primarily to solve some geometrical problems. In fact, at a later stage a constant has been defined to be the supremum taken with respect to the convex bounded subsets C of a Banach space X, of the ratio between the Chebyshev radius of C relative to C, and the diameter of C, which has close connection with normal structure. However, besides serious subsequent theoretical investigations on this concept of Brodskii and Milman and related ideas developed later on, the concept of normal structure becomes dominant in the theory of fixed points of operators, specially for nonexpansive mappings.
机译:Brodskii和Milman引入了正常结构的定义,主要是为了解决一些几何问题。实际上,在以后的阶段,常数被定义为相对于Banach空间X的凸有界子集C的最高值,即C的切比雪夫半径与C的比值与C的直径之比,与正常结构有紧密的联系。但是,除了随后对Brodskii和Milman的概念进行了认真的理论研究以及后来发展的相关思想之外,法线结构的概念在算子不动点理论中也占主导地位,特别是对于非扩展映射。

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