Abstract
Let
(Ω,Σ) be a measurable space,
X and
Y separable Banach spaces, and
C a weakly compact subset of
X. Let
f
:
Ω×C→Y
and
T
:
Ω×C→Y
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.