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Keywords:
Banach algebra; fixed point theorem; integral equations
Banach algebra; fixed point theorem; integral equations
Summary:
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.).
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