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.

Abstract

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 r≥−1 being a given integer. A concrete application of the results obtained is presented.