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We study the problem of solvability of the equation
\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.