On an abstract analog of the Krylov-Bogolyubov transformation in the theory of perturbations of linear operators (Q1966307)

The paper deals with the family of operators \(L=A+\varepsilon F\), where \(A\) is a closed densely defined linear operator in a Banach space \(X\), \(F\) is a nonlinear map in \(X\) which satisfies a Lipschitz-type condition and \(\varepsilon\) is a small parameter. The authors describes an abstract analogue of the Krylov-Bogolyubov transformation for the ``perturbed'' operator \(L\) and studies some properties of such a transformation. The paper contains no proofs.