Random fixed point theorems under weak topology features and application to random integral equations with lack of compactness

Abstract

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.