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Integrable solutions of a functional-integral equation. (English) Zbl 0755.45005
A theorem about the existence of solutions of the functional-integral equation (1) \(x(t)=f\left(t,\int^ 1_ 0k(t,s)g(s,x(s))ds\right)\), \(t\in[0,1]\), is proved. The technique used in the proof depends on an interesting conjunction of the notions of the measure of weak noncompactness and the Schauder fixed point principle.
It is worth while to mention that the existence theorem for (1) is proved under rather general and natural hypotheses.

MSC:
45G10 Other nonlinear integral equations
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