Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in Lp Spaces
Abstract
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 existence and uniqueness of solution in $L^p([a,b])$, with {$1<p<\infty$}.We use Banach Fixed Point Theorem and employ the successive approximation method and Chebyshev quadrature for approximating the values of integrals. Finally, to illustrate the results of this work, we provide some numerical examples.
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PDFDOI: https://doi.org/10.5540/tema.2019.020.03.403
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Trends in Computational and Applied Mathematics
A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
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