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Zeitschrift für Analysis und ihre Anwendungen


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Volume 15, Issue 4, 1996, pp. 935–948
DOI: 10.4171/ZAA/738

Published online: 1996-12-31

On a Class of Multilinear Operator Equations

Jaan Janno[1] and Lothar von Wolfersdorf

(1) Tallin Technical University, Estonia

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.

Keywords: Nonlinear operator equations, scale of norms, existence, stability

Janno Jaan, von Wolfersdorf Lothar: On a Class of Multilinear Operator Equations. Z. Anal. Anwend. 15 (1996), 935-948. doi: 10.4171/ZAA/738