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

Let (Ω,Σ) be a measurable space, X and Y separable Banach spaces, and C a weakly compact subset of X. Let View the MathML source and View the MathML source be continuous random operators. Then the deterministic solvability of the equation f(ω,x)−T(ω,x)=0(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 ω∈Ω. As applications, random fixed points of various types of pseudo-contractive and k-set-contractive random operators are obtained.