最近点映射到一致凸集上

IF 0.9 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI:10.1007/s10114-025-3598-3

Qingjin Cheng, Cuiling Wang, Jianjian Wang

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引用次数: 0

摘要

设K是Banach空间X的一个（有界）闭一致凸子集，我们证明了(i)最近点映射是定义良好的，并且从X到K总是连续的，（ii）存在一个自反空间Y，它在每个方向范数上都是一致的圆，使得Y包含K作为子集和最近点映射PK；Y→K从任何包含K到K的有界集合一致连续。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Nearest Point Maps onto Uniformly Convex Sets

Let K be a (bounded) closed uniformly convex subset of a Banach space X. We show that

(i)
the nearest point map is well-defined and always continuous from X onto K,
(ii)
there is a reflexive space Y with a uniform rotund in every direction norm such that Y contains K as a subset and the nearest point map P_K: Y → K is uniformly continuous from any bounded set containing K onto K.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.