Affiliation:
1. Institute of Mathematics , University of Silesia , Bankowa 14 , Katowice , Poland
Abstract
Abstract
We study the problem of solvability of the equation
ϕ
(
x
)
=
∫
Ω
g
(
w
)
ϕ
(
f
(
x
,
ω
)
)
P
(
d
ω
)
+
F
(
x
)
,
\varphi \left( x \right) = \int_\Omega {g\left( w \right)} \varphi \left( {f\left( {x,\omega } \right)} \right)P\left( {d\omega } \right) + F\left( x \right),
where P is a probability measure on a σ-algebra of subsets of Ω, assuming Hölder continuity of F on the range of f.
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