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


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.


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

Full Text:


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

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

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)

Indexed in:



Desenvolvido por:

Logomarca da Lepidus Tecnologia