The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations

We study the solvability of some nonlinear functional integral equations in the Banach algebra of real functions defined, continuous, and bounded on the real half axis. We apply the technique of measures of noncompactness in order to obtain existence results for equations in question. Additionally,...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.632-646-672
Main Authors: Banas, Józef, Dudek, Szymon
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Banach spaces
Integral equations
Mathematical analysis
Mathematical research
Nonlinear theories
Nonlinearity
Studies
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Summary:We study the solvability of some nonlinear functional integral equations in the Banach algebra of real functions defined, continuous, and bounded on the real half axis. We apply the technique of measures of noncompactness in order to obtain existence results for equations in question. Additionally, that technique allows us to obtain some characterization of considered integral equations. An example illustrating the obtained results is also included.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/537897