Implicit functions, nonlinear integral equations, and the measure of noncompactness of the superposition operator. (English) Zbl 0495.45007

Appell, Jürgen

J. Math. Anal. Appl. 83, 251-263 (1981).

MSC:

45G10	Other nonlinear integral equations
45P05	Integral operators
47H10	Fixed-point theorems
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
58C15	Implicit function theorems; global Newton methods on manifolds

Keywords:

superposition operator; Urysohn operator; Hammerstein operator; Schauder fixed point principle; Hausdorff measure of noncompactness; Banach space; noncompact integral operators of Hammerstein form; abstract implicit function theorem; invertible asymptotic linearization

References:

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