# zbMATH — the first resource for mathematics

Integrable solutions of a functional-integral equation. (English) Zbl 0679.45003
Under certain assumptions on the functions f,g,k the authors prove that the functional-integral equation $x(t)=g(t)+f(t,\int^{1}_{0}k(t,s)x(\phi (s))ds),$ $$t\in [0,1)$$ has at least one solution $$x\in L^ 1[0,1]$$, which is a.e. nonincreasing on $$L^ 1[0,1]$$. The method of proof is based on the notion of measure of weak noncompactness and the fixed point theorem due to G. Emmanuele [Bull. Math. Soc. Sci. Math. Répub. Soc. Roum., Nouv. Sér. 25, 353- 358 (1981; Zbl 0482.47027)].
Reviewer: J.Kolomý

##### MSC:
 45G10 Other nonlinear integral equations 47J25 Iterative procedures involving nonlinear operators
Zbl 0482.47027
Full Text: