| Popis: |
The paper consists of two parts. At first, assuming that (Ω, A, P) is a probability space and (X, ϱ) is a complete and separable metric space with the σ-algebra of all its Borel subsets we consider the set c of all ⊗ 𝒜-measurable and contractive in mean functions f : X × Ω → X with finite integral ∫ Ω ϱ (f(x, ω), x) P (dω) for x ∈ X, the weak limit π f of the sequence of iterates of f ∈ c, and investigate continuity-like property of the function f ↦ πf, f ∈ c, and Lipschitz solutions φ that take values in a separable Banach space of the equation |
