标题： 随机赋范模中的随机Kakutani不动点定理 显示英文标题

标题： The random Kakutani fixed point theorem in random normed modules

摘要： 基于最近发展的随机序列紧性理论，我们证明了随机赋范模中的随机Kakutani不动点定理：如果G是随机赋范模中一个随机序列紧的L0-凸子集，则每个-Tc上半连续映射F:G→2G，使得对于每个x在G中，F(x)是闭的且L0-凸的，都有一个不动点。 这是随机赋范模中集合值映射的第一个不动点定理，提供了经典Kakutani不动点定理的随机推广，以及Math. Ann. 391(3), 3863--3911 (2025)中建立的非紧Schauder不动点定理的集合值扩展。 显示英文摘要

摘要： Based on the recently developed theory of random sequential compactness, we prove the random Kakutani fixed point theorem in random normed modules: if G is a random sequentially compact L0-convex subset of a random normed module, then every -stable Tc-upper semicontinuous mapping F:G to 2G such that F(x) is closed and L0-convex for each x in G, has a fixed point. This is the first fixed point theorem for set-valued mappings in random normed modules, providing a random generalization of the classical Kakutani fixed point theorem as well as a set-valued extension of the noncompact Schauder fixed point theorem established in Math. Ann. 391(3), 3863--3911 (2025).