On a generalization of the Schauder and Krasnosel'skii fixed points theorems on Dunford–Pettis spaces and applications

In this paper, we give a generalization of the Schauder and Krasnosel'skii fixed point theorems in Dunford–Pettis spaces. Both of these theorems can be used to resolve some open problems posed by Jeribi (Nonlinear Anal.: Real World Appl. 2002; 3 :85–105); and Latrach (J. Math. Phys. 1996; 37 :1336–1348). Further, we applied our work to prove some existence results for a source problem with general boundary conditions in L₁ spaces. Copyright © 2005 John Wiley & Sons, Ltd.