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Zeitschrift für Analysis und ihre Anwendungen


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Volume 14, Issue 1, 1995, pp. 89–93
DOI: 10.4171/ZAA/664

Published online: 1995-03-31

Some Remarks on the Hildebrandt-Graves Theorem

A. Vignoli[1] and Petr P. Zabrejko[2]

(1) Università di Roma 'Tor Vergata', Italy
(2) Belgos University, Minsk, Belarus

This paper is concerned with a generalization of the Hildebrandt-Graves implicit function theorem building on a weaker acting condition for the derivative of the nonlinear operator involved. The abstract theorem is illustrated by means of an application to nonlinear singular integral equations where classical implicit function theorems do not apply.

Keywords: Implicit functions, Hildebrandt-Graves theorem, singular integral equations

Vignoli A., Zabrejko Petr: Some Remarks on the Hildebrandt-Graves Theorem. Z. Anal. Anwend. 14 (1995), 89-93. doi: 10.4171/ZAA/664