Geodesic
On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock–Kurzweil integrals
Aneta Sikorska-Nowak1
1 Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87, 61-614 Poznań, Poland
Annales Polonici Mathematici, Tome 83 (2004) no. 3, pp. 257-267.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove some existence theorems for nonlinear integral equations of the Urysohn type $x(t)=\varphi (t)+\lambda \int _0^a f(t,s,x(s))\, ds$ and Volterra type $x(t)=\varphi (t)+\int _0^tf(t,s,x(s))\, ds$, $t\in I_a=[0,a]$, where $f$ and $\varphi $ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock–Kurzweil integral.
DOI : 10.4064/ap83-3-7
Keywords: prove existence theorems nonlinear integral equations urysohn type varphi lambda int s volterra type varphi int s where varphi functions values banach spaces fundamental tools measures noncompactness properties henstock kurzweil integral

Aneta Sikorska-Nowak 1

1 Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87, 61-614 Poznań, Poland 
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Aneta Sikorska-Nowak. On the existence of solutions
 of nonlinear integral equations in Banach spaces
 and Henstock–Kurzweil integrals. Annales Polonici Mathematici, Tome 83 (2004) no. 3, pp. 257-267. doi : 10.4064/ap83-3-7. http://geodesic.mathdoc.fr/articles/10.4064/ap83-3-7/

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