On a Class of Multilinear Operator Equations

Abstract

By means of contraction principle in a Banach space $E$ with a scale of norms $\| \cdot \|_{\sigma} (\sigma ≥ 0)$ 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 equations with operators of generalized convolution type.