关于\(\operatorname{CAT}(0)\)空间中平均映射的一个概念

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2022-07-29 DOI:10.1134/S0016266322010038

A. Bërdëllima

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引用次数: 0

摘要

我们在更广泛的\(\operatorname{CAT}(0)\)空间类中引入了平均映射的概念。我们称这些映射为\(\alpha\) -坚定非扩张性，并为那些拟\(\alpha\) -坚定非扩张性且有一个公共不动点的映射发展了基本的微积分规则。我们证明了当\(T\)是准\(\alpha\) -坚定非可扩张时，非可扩张映射\(T\)的迭代\(x_n:=Tx_{n-1}\)弱收敛到\(\operatorname{Fix} T\)中的一个元素。而且，\(P_{\operatorname{Fix} T}x_n\)强收敛于这个弱极限。我们的理论用两个经典的循环和平均投影的例子来说明。

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On a Notion of Averaged Mappings in \(\operatorname{CAT}(0)\) Spaces

We introduce a notion of averaged mappings in the broader class of \(\operatorname{CAT}(0)\) spaces. We call these mappings \(\alpha\)-firmly nonexpansive and develop basic calculus rules for ones that are quasi-\(\alpha\)-firmly nonexpansive and have a common fixed point. We show that the iterates \(x_n:=Tx_{n-1}\) of a nonexpansive mapping \(T\) converge weakly to an element in \(\operatorname{Fix} T\) whenever \(T\) is quasi-\(\alpha\)-firmly nonexpansive. Moreover, \(P_{\operatorname{Fix} T}x_n\) converge strongly to this weak limit. Our theory is illustrated with two classical examples of cyclic and averaged projections.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.