长度空间非自非线性收缩的定点定理

Pub Date : 2024-03-03 DOI:10.12775/tmna.2023.007

Simeon Reich, A. Zaslavski

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引用次数: 0

摘要

1988 年，阿萨德（N.A. Assad）证明，将完全度量凸空间的封闭子集带入该空间，使该子集的边界映射回子集本身的非自身非线性收缩有一个唯一的固定点。在本文中，我们将完整度量凸空间替换为长度空间的完整度量空间，从而扩展了这一结果。

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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A fixed point theorem for nonself nonlinear contractions in length spaces

In 1988 N.A. Assad showed that a nonself nonlinear contraction taking a closed subset of a complete metrically convex space into the space so that the boundary of this subset is mapped back into the subset itself has a unique fixed point. In the present paper we extend this result by replacing the complete metrically convex space with a complete metric space which is a length space.

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