Invariant measures for random expanding on average Saussol maps

In this paper, we investigate the existence of random absolutely continuous invariant measures (ACIP) for expanding on average Saussol maps in higher dimensions. This is done by establishment a Lasota–Yorke inequality transfer operators space bounded oscillation. We prove that number ergodic skew product ACIPs finite and will provide an upper bound these ACIPs. work can be seen as generalization [F. Batayneh C. González-Tokman, On dimensions, Discrete Contin. Dyn. Syst. 41 (2021) 5887–5914] admissible Jabłoński to more general class higher-dimensional maps.