On existence of extremal solutions of nonlinear functional integral equations in Banach algebras.

Dhage, B.C.

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Displaying similar documents to “On existence of extremal solutions of nonlinear functional integral equations in Banach algebras.”

On some nonlinear alternatives of Leray-Schauder type and functional integral equations

Bapurao Chandra Dhage (2006)

Archivum Mathematicum

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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....

Furi–Pera fixed point theorems in Banach algebras with applications

Smaïl Djebali, Karima Hammache (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this work, we establish new Furi–Pera type fixed point theorems for the sum and the product of abstract nonlinear operators in Banach algebras; one of the operators is completely continuous and the other one is $𝒟$ -Lipchitzian. The Kuratowski measure of noncompactness is used together with recent fixed point principles. Applications to solving nonlinear functional integral equations are given. Our results complement and improve recent ones in [10], [11], [17].