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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