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    Integrable solutions of a generalized mixed-type functional integral equation

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    In this work, we prove the existence of integrable solutions for the following generalized mixed-type nonlinear functional integral equation x(t)=g(t,(Tx)(t))+f(t,∫0tk(t,s)u(t,s,(Qx)(s))β€…β€Šds),β€…β€Št∈[0,∞).x(t)=g\left(t,(Tx)(t)\right)+f\left(t,\int_0^t k(t,s)u(t,s,(Qx)(s))\;ds\right),\;t\in[0,\infty). Our result is established by means of a Krasnosel'skii type fixed point theorem proved in [M.A. Taoudi: \textit{Integrable solutions of a nonlinear functional integral equation on an unbounded interval}, Nonlinear Anal. 71 (2009) 4131-4136]. In the last section we give an example to illustrate our result.Comment: 25 page
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