On a Fredholm-Volterra integral equation

Alexandru-Darius Filip, Ioan Rus

Abstract


In this paper we give conditions in which the integral equation \centerline{$x(t)=\displaystyle\int_a^c K(t,s,x(s))ds+\int_a^t H(t,s,x(s))ds+g(t),\ t\in [a,b],$} \noindent where $a<c<b$, $K\in C([a,b]\times [a,c]\times \mathbb{B},\mathbb{B})$, $H\in C([a,b]\times [a,b]\times \mathbb{B},\mathbb{B})$, $g\in C([a,b],\mathbb{B})$, with $\mathbb{B}$ a (real or complex) Banach space, has a unique solution in $C([a,b],\mathbb{B})$. An iterative algorithm for this equation is also given.

Keywords


Fredholm-Volterra integral equation; existence; uniqueness; contraction; fiber contraction

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DOI: http://dx.doi.org/10.24193/subbmath.2021.3.12

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