About the existence of integrable solutions of a functional-integral equation. (English) Zbl 0746.45004

The author proves the existence of integrable solutions for a class of functional-integral equations of the type \(x(t)=g(t)+f\left(t,\int_ 0^ 1 k(t,s)x(\varphi(s))ds\right)\), \(t\in[0,1]\), which arises in different applications. He improves a previous result by J. Banaś and Z. Knap [Integrable solutions of a functional-integral equation, ibid. 2, No. 1, 31-38 (1989; Zbl 0679.45003)]. Basically, he deletes some kind of assumptions on the monotonicity of \(g\), \(f\) and \(k\). In the proof, the Tikhonov fixed point theorem is used.


45G10 Other nonlinear integral equations
47J05 Equations involving nonlinear operators (general)


Zbl 0679.45003
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