Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 917614, 13 pages
doi:10.1155/2009/917614
Convex solutions of a nonlinear integral equation of Urysohn type
Tiberiu Trif
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Str. Kogă\ln iceanu Nr. 1, 400084 Cluj-Napoca, Romania
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.