Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 917614, 13 pages
Research Article

Convex Solutions of a Nonlinear Integral Equation of Urysohn Type

Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Str. Kogălniceanu Nr. 1, 400084 Cluj-Napoca, Romania

Received 4 August 2009; Accepted 25 September 2009

Academic Editor: Donal O'Regan

Copyright © 2009 Tiberiu Trif. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the solvability of a nonlinear integral equation of Urysohn type. Using the technique of measures of noncompactness we prove that under certain assumptions this equation possesses solutions that are convex of order p for each p{1,0,,r}, with r1 being a given integer. A concrete application of the results obtained is presented.