A noncompact Schauder fixed point theorem in random normed modules and its applications

Release time:2024-10-18

Impact Factor:1.3

DOI number:10.1007/s00208-024-03017-1

Journal:Math. Ann.

Funded by:国家自然科学基金

Abstract: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.

Co-author:Yachao Wang, Hong-kun Xu, George Xianzhi Yuan, Goong Chen

First Author:Tiexin Guo

Indexed by:Journal paper

Discipline:Natural Science

First-Level Discipline:Mathematics

Document Type:J

ISSN No.:0025-5831

Translation or Not:no

Date of Publication:2024-10-18

Included Journals:SCI

Links to published journals:https://link.springer.com/article/10.1007/s00208-024-03017-1