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In this work we consider the general functional-integral equation:\begin{equation*} y(t) = f\left(t, \int_{a}^{b} k(t,s)g(s,y(s))ds\right),\qquad t\in [a,b], \end{equation*} and give conditions that guarantee existenceand uniqueness of solution in $L^p([a,b])$, with $1<p<\infty$. We use BanachFixed Point Theorem} and employ the successive approximation method andChebyshev quadrature for approximating the values of integrals. Finally, toillustrate the results of this work, we provide some numerical examples.

Existence, uniqueness, and approximation for solutions of a functional-integral equation in $L^p$ spaces