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An existence theorem for the Urysohn integral equation in Banach spaces. (English) Zbl 0546.45011
By applying fixed point theorems and measures of non-compactness, the author proves the solvability of a nonlinear integral equation of Urysohn type in a generalized Orlicz space of Banach-space valued functions.
Reviewer: J.Appell

MSC:
45N05 Abstract integral equations, integral equations in abstract spaces
45G10 Other nonlinear integral equations
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
47J05 Equations involving nonlinear operators (general)
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