JournalszaaVol. 15, No. 4pp. 935–948

On a Class of Multilinear Operator Equations

  • Jaan Janno

    Tallin Technical University, Estonia
  • Lothar von Wolfersdorf

    Technische Universität, Freiberg, Germany
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Abstract

By means of contraction principle in a Banach space EE with a scale of norms σ(σ0)\| \cdot \|_{\sigma} (\sigma ≥ 0) existence, uniqueness and stability of solutions are proved for a general class of operator equations u+G0u+G1u=gu + G_0u + G_1u = g including multilinear ones where G0,G1(EE)G_0, G_1 \in (E \to E) are some operators. The theorems are applicable to equations with operators of generalized convolution type.

Cite this article

Jaan Janno, Lothar von Wolfersdorf, On a Class of Multilinear Operator Equations. Z. Anal. Anwend. 15 (1996), no. 4, pp. 935–948

DOI 10.4171/ZAA/738