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

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  • Józef Banaś
  • Szymon Dudek

Abstract

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.

Suggested Citation

  • Józef Banaś & Szymon Dudek, 2013. "The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-15, April.
    • Handle: RePEc:hin:jnlaaa:537897
    DOI: 10.1155/2013/537897
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    Cited by:

    1. Ahmed M. A. El-Sayed & Eman M. A. Hamdallah & Malak M. S. Ba-Ali, 2022. "On the De Blasi Measure of Noncompactness and Solvability of a Delay Quadratic Functional Integro-Differential Equation," Mathematics, MDPI, vol. 10(9), pages 1-11, April.

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