Lipschitzian solutions to inhomogeneous linear iterative equations

We study the problems of the existence, uniqueness and continuous dependence of Lipschitzian solutions $φ$ of equations of the form $φ(x)=\int_Ωg(ω)φ\big(f(x,ω)\big)μ(dω)+F(x),$ where $μ$ is a measure on a $σ$-algebra of subsets of a set $Ω$.

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