Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in Lp Spaces

Suzete M Afonso, Juarez S Azevedo, Mariana P. G. da Silva, Adson M Rocha

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.


Keywords


Functional-integral equations, $L^p$ spaces, Existence, Uniqueness, Successive approximation.

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DOI: https://doi.org/10.5540/tema.2019.020.03.403

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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