Extended Cartan fixed point theorem

被引：0

作者：

Bancha Panyanak

Watchareepan Atiponrat

Warunun Inthakon

Attapol Kaewkhao

Narawadee Phudolsitthiphat

Jaturon Wattanapan

Teerapong Suksumran

机构：

[1] Chiang Mai University,Department of Mathematics, Faculty of Science

来源：

Journal of Fixed Point Theory and Applications | 2022年 / 24卷

关键词：

Fixed point theorem; gyrogroup action; CAT(0); orthogonal projection; bounded function; Primary 54H25; Secondary 54E35; 20N05; 05A05;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The well-known Cartan fixed point theorem states that if a group G acts isometrically on a complete CAT(0) space and if G has a bounded orbit, then G has a fixed point. In this article, we extend the Cartan fixed point theorem to the case of gyrogroups—non-associative structures that generalize groups. We also give a prominent class of isometric gyrogroup actions on a suitable subspace of the space of bounded functions from a gyrogroup to a metric space.

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