On a class of multilinear operator equations (Q2365272)

Summary: By means of a contraction principle in a Banach space \(E\) with a scale of norms \(|\cdot|_\sigma\) \((\sigma\geq 0)\) existence, uniqueness and stability of solutions are proved for a general class of operator equations \(u+G_0u+G_1u=g\) including multilinear ones where \(G_0,G_1\in (E\to E)\) are some operators. The theorems are applicable to questions with operators of generalized convolution type.