The fixed point theorems and invariant approximations for random nonexpansive mappings in random normed modules
发布时间：2024-10-25
点击次数：
DOI码：10.1016/j.jmaa.2023.127796
发表刊物：J. Math. Anal. Appl.
关键字：Random normed modules Random sequential compactness Random nonexpansive mappings Dotson fixed point theorem Invariant approximations
摘要：By making full use of the theory of random sequential compactness in random normed modules, in this paper we establish a noncompact Dotson fixed point theorem: if C is a σ–stable random sequentially compact L0–star–shaped subset of a random normed module, then every random nonexpansive mapping T : C → C has a fixed point. Furthermore, we obtain an existence result for best approximations in random normed modules: let E be a random normed module, T : E → E a random nonexpansive mapping with a fixed point u and C a closed, σ–stable and T –invariant subset of E such that T (C)israndom sequentially compact, then the set of best approximations of u in C is nonempty, which generalizes the classical result of Smoluk. In addition, we also get an existence result for invariant approximations in random normed modules. A significant distinction between the proofs of our results in random normed modules and the corresponding classical results in normed spaces is that the σ–stability of both the sets and mappings involved in the random setting plays a prominent part in the proofs of the main results of this paper.
合写作者：Yachao Wang, Tiexin Guo
论文类型：期刊论文
论文编号：127796
学科门类：理学
一级学科：数学
文献类型：J
卷号：531
ISSN号：0022-247X
是否译文：否
发表时间：2023-09-22
收录刊物：SCI
发布期刊链接：https://www.sciencedirect.com/science/article/pii/S0022247X23007990?via%3Dihub