一致局部压缩映射的收敛性和适定性

IF 0.7 4区数学 Q2 MATHEMATICS

Topological Methods in Nonlinear Analysis Pub Date : 2023-07-16 DOI:10.12775/tmna.2022.035

S. Reich, A. Zaslavski

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引用次数: 0

摘要

E.Rakoch在1961年的一篇论文中证明了一致局部压缩映射具有不动点。在本文中，我们证明了对于这样的映射，不动点问题是适定的，并且这样的映射的不精确迭代在有界集上一致地收敛到它的唯一不动点。利用孔隙率的概念，我们还证明了大多数一致局部非扩张映射实际上是一致局部收缩的。

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Convergence and well-posedness properties of uniformly locally contractive mappings

In a 1961 paper by E. Rakotch it was shown that a uniformly locally contractive mapping has a fixed point. In the present paper we show that for such a mapping, the fixed point problem is well posed and that inexact iterates of such a mapping converge to its unique fixed point, uniformly on bounded sets. Using the porosity notion, we also show that most uniformly locally nonexpansive mappings are, in fact, uniformly locally contractive.

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来源期刊

Topological Methods in Nonlinear Analysis 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.