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On some nonlinear alternatives of Leray-Schauder type and functional integral equations
Archivum mathematicum, Tome 42 (2006) no. 1, pp. 11-23 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, some new fixed point theorems concerning the nonlinear alternative of Leray-Schauder type are proved in a Banach algebra. Applications are given to nonlinear functional integral equations in Banach algebras for proving the existence results. Our results of this paper complement the results that appear in Granas et. al. (Granas, A., Guenther, R. B. and Lee, J. W., Some existence principles in the Caratherodony theory of nonlinear differential system, J. Math. Pures Appl. 70 (1991), 153–196.) and Dhage and Regan (Dhage, B. C. and O’Regan, D., A fixed point theorem in Banach algebras with applications to functional integral equations, Funct. Differ. Equ. 7(3-4)(2000), 259–267.).
In this paper, some new fixed point theorems concerning the nonlinear alternative of Leray-Schauder type are proved in a Banach algebra. Applications are given to nonlinear functional integral equations in Banach algebras for proving the existence results. Our results of this paper complement the results that appear in Granas et. al. (Granas, A., Guenther, R. B. and Lee, J. W., Some existence principles in the Caratherodony theory of nonlinear differential system, J. Math. Pures Appl. 70 (1991), 153–196.) and Dhage and Regan (Dhage, B. C. and O’Regan, D., A fixed point theorem in Banach algebras with applications to functional integral equations, Funct. Differ. Equ. 7(3-4)(2000), 259–267.).
Classification : 45G10, 47H10, 47N20
Keywords: Banach algebra; fixed point theorem; integral equations 
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Dhage, Bapurao Chandra. On some nonlinear alternatives of Leray-Schauder type and functional integral equations. Archivum mathematicum, Tome 42 (2006) no. 1, pp. 11-23. http://geodesic.mathdoc.fr/item/ARM_2006_42_1_a1/

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