Existence criteria for integral equations in Banach spaces


The paper contains a few existence results concerning nonlinear integral equations of Volterra and Uryson type in Banach spaces. It is assumed that the kernel \(f(t,s,x)\) of both integral equations satisfies Carathéodory-type conditions and \(\mu (f(t,s,M))\leq \omega (t,s,\mu(M))\) for all \(t,s\in[0,T]\) and for any bounded subset M of a Banach space E. Here μ denotes the Kuratowski or Hausdorff measure of noncompactness. Special cases of the mentioned integral equations are also studied in detail.


Donal O’Regan,

Radu Precup
Babeş-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania


Volterra and Urysohn integral equations in abstract spaces; Measure of noncompactness; Continuation method; Fixed point

Cite this paper as:

D. O’Regan, R. Precup, Existence criteria for integral equations in Banach spaces, J. Inequal. Appl. 6 (2001), 77-97, http://dx.doi.org/10.1155/S1025583401000066


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Journal of Inequalities and Applications

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MR 2003c:45007, Zbl 0993.45011


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