# zbMATH — the first resource for mathematics

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)
Full Text: