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

Authors

  • Suzete M Afonso
  • Juarez S Azevedo Universidade Federal do Recôncavo da Bahia
  • Mariana P. G. da Silva
  • Adson M Rocha

DOI:

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

Keywords:

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

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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Published

2019-12-02

How to Cite

Afonso, S. M., Azevedo, J. S., da Silva, M. P. G., & Rocha, A. M. (2019). Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in Lp Spaces. Trends in Computational and Applied Mathematics, 20(3), 403. https://doi.org/10.5540/tema.2019.020.03.403

Issue

Vol. 20 No. 3 (2019)

Section

Original Article

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