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By means of the contraction principle we prove existence, uniqueness and stability of solutions for nonlinear equations u + G0 [D, tL] + L(G 1 [D, u], G 2 [D, uJ) = f in a Banach space E, where Go, C 1 , C2 satisfy Lipschitz conditions in scales of norms, L is a bilinear operator and D is a data parameter. The theory is applicable for inverse problems of memory identification and generalized convolution equations of the second kind.

Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales