Displaying similar documents to “Furi–Pera fixed point theorems in Banach algebras with applications”

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....

Fixed Point Theorems of the Banach and Krasnosel’skii Type for Mappings on m -tuple Cartesian Product of Banach Algebras and Systems of Generalized Gripenberg’s Equations

Eva Brestovanská, Milan Medveď (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we prove some fixed point theorems of the Banach and Krasnosel’skii type for mappings on the m -tuple Cartesian product of a Banach algebra X over ℝ . Using these theorems existence results for a system of integral equations of the Gripenberg’s type are proved. A sufficient condition for the nonexistence of blowing-up solutions of this system of integral equations is also proved.