Geodesic
Existance of solutions of nonlinear integral equations and Henstock–Kurzweil integrals
Commentationes Mathematicae, Tome 47 (2007) no. 2, pp. 227-238.

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We prove an existence theorems for the nonlinear integral equation \[ x(t) = f (t) + \int_{0}^a k_1 (t, s)x(s)ds + \int_{0}^a k_2(t, s)g(s, x(s))ds,\quad t \in I_a = [0, a], a \in \mathbb{R} _+, \] where \(f, g, x\) are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.
DOI : 10.14708/cm.v47i2.5252
Mots-clés : existence of solution, measure of noncompactness, nonlinear Fredholm integral equation, Henstock-Kurzweil integral, HL integral 
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Aneta Sikorska-Nowak. Existance of solutions of nonlinear integral equations and Henstock–Kurzweil integrals. Commentationes Mathematicae, Tome 47 (2007) no. 2, pp.  227-238. doi : 10.14708/cm.v47i2.5252. http://geodesic.mathdoc.fr/articles/10.14708/cm.v47i2.5252/

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