Sonia Hajjem - Academia.edu (original) (raw)
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Papers by Sonia Hajjem
Applied Mathematics and Computation, 2010
In this paper, we consider a compact interval ½a; b, a positive real number p P 1 and give differ... more In this paper, we consider a compact interval ½a; b, a positive real number p P 1 and give different existence results for L p ð½a; bÞ and Cð½a; bÞ-solutions of some nonlinear integral equations of the Hammerstein and Volterra types. The main ingredients of our existence results are the Shaefer's and Schauder's fixed point theorems combined with a general version of Gronwall's inequality. Moreover, we give a numerical method for the approximation of the solutions of the Volterra-Hammerstein integral equations. Finally, to illustrate the results of this work, we provide the reader with some numerical examples.
Applied Mathematics and Computation, 2010
In this paper, we consider a compact interval ½a; b, a positive real number p P 1 and give differ... more In this paper, we consider a compact interval ½a; b, a positive real number p P 1 and give different existence results for L p ð½a; bÞ and Cð½a; bÞ-solutions of some nonlinear integral equations of the Hammerstein and Volterra types. The main ingredients of our existence results are the Shaefer's and Schauder's fixed point theorems combined with a general version of Gronwall's inequality. Moreover, we give a numerical method for the approximation of the solutions of the Volterra-Hammerstein integral equations. Finally, to illustrate the results of this work, we provide the reader with some numerical examples.