We present several random fixed point theorems for random operators with deterministic or stochastic domains. The main assumptions of our results are formulated in terms of the weak topology and an axiomatic definition of the measure of weak noncompactness. The results herein extend in a broad sense some new and classical results in the literature. As an application, we discuss the solvability of a random Hammerstein integral equation with lack of compactness.

中文翻译：

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弱拓扑特征下的随机不动点定理及其在缺乏紧性的随机积分方程中的应用

我们为具有确定性或随机域的随机算子提供了几个随机不动点定理。我们的结果的主要假设是根据弱拓扑和弱非紧实度度量的公理定义来表述的。本文的结果在广义上扩展了文献中的一些新的和经典的结果。作为一种应用，我们讨论了缺乏紧凑性的随机Hammerstein积分方程的可解性。