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

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

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

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Veröffentlicht in:arXiv.org 2018-09
Hauptverfasser: Afonso, Suzete M, Azevedo, Juarez S, Mariana P G da Silva, Rocha, Adson M
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Chebyshev approximation
Fixed points (mathematics)
Integral equations
Uniqueness
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Zusammenfassung: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
ISSN:2331-8422