The solvability of the nonlinear implicit equation in Banach spaces is examined. Theorem 1 covers situations in which does not exist, but can be approximated by means of mappings with better properties. Theorem 2 is of Moser-Nash type. In order to obtain optimal regularity results the Newton iteration method is combined with a triple approximation technique using smoothing operators and properties of certain interpolation spaces.
Cite this article
Matthias Günther, Zwei Versionen von verallgemeinerten Sätzen über implizite Funktionen. Z. Anal. Anwend. 5 (1986), no. 6, pp. 491–506