Random fixed points of K-set- and pseudo-contractive random maps

Let $\text{(Ω,Σ)}$ be a measurable space, X and Y separable Banach spaces, and C a weakly compact subset of X. Let $\text{f}\text{:}\text{Ω×C→Y}$ and $\text{T}\text{:}\text{Ω×C→Y}$ be continuous random operators. Then the deterministic solvability of the equation$\text{f(ω,x)−T(ω,x)=0}\text{(ω∈Ω,x∈C)}$implies the stochastic solvability of it provided that (f−T)(ω,.) is demiclosed at zero and T(ω,C) is bounded for each $\text{ω∈Ω}$. As applications, random fixed points of various types of pseudo-contractive and k-set-contractive random operators are obtained.