A noncompact Schauder fixed point theorem in random normed modules and its applications
发布时间：2024-10-18
点击次数：
影响因子：1.3
DOI码：10.1007/s00208-024-03017-1
发表刊物：Math. Ann.
项目来源：国家自然科学基金
摘要：Motivated by the randomized version of the classical Bolzano–Weierstrass theorem, in this paper we first introduce the notion of a random sequentially compact set in a random normed module and develop the related theory systematically. From these developments, we prove the corresponding Schauder fixed point theorem: let E be a random normed module and G arandom sequentially compact L0-convex set of E, then every σ-stable continuous mapping from G to G has a fixed point, which unifies all the previous random generalizations of the Schauder fixed point theorem. As one of the applications of the theorem, we prove the existence of Nash equilibrium points in the context of conditional information. It should be pointed out that the main challenge in this paper lies in overcoming noncompactness since a random sequentially compact set is generally noncompact.
合写作者：Yachao Wang, Hong-kun Xu, George Xianzhi Yuan, Goong Chen
第一作者：Tiexin Guo
论文类型：期刊论文
学科门类：理学
一级学科：数学
文献类型：J
ISSN号：0025-5831
是否译文：否
发表时间：2024-10-18
收录刊物：SCI
发布期刊链接：https://link.springer.com/article/10.1007/s00208-024-03017-1