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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 819315, 14 pages
Review Article

Compactness Conditions in the Study of Functional, Differential, and Integral Equations

1Department of Mathematics, Rzeszów University of Technology, Aleja Powstańców Warszawy 8, 35-959 Rzeszów, Poland
2Departamento de Mathemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain

Received 13 December 2012; Accepted 2 January 2013

Academic Editor: Beata Rzepka

Copyright © 2013 Józef Banaś and Kishin Sadarangani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [7 citations]

The following is the list of published articles that have cited the current article.

  • S.A. Mohiuddine, M. Mursaleen, and A. Alotaibi, “The Hausdorff measure of noncompactness for some matrix operators,” Nonlinear Analysis: Theory, Methods & Applications, vol. 92, pp. 119–129, 2013. View at Publisher · View at Google Scholar
  • Mohamed Abdalla Darwish, Józef Banaś, and Ebraheem O. Alzahrani, “The Existence and Attractivity of Solutions of an Urysohn Integral Equation on an Unbounded Interval,” Abstract and Applied Analysis, vol. 2013, pp. 1–9, 2013. View at Publisher · View at Google Scholar
  • Mariusz Gil, and Stanisław Wędrychowicz, “Schauder-Tychonoff Fixed-Point Theorem in Theory of Superconductivity,” Journal of Function Spaces and Applications, vol. 2013, pp. 1–12, 2013. View at Publisher · View at Google Scholar
  • Orlando Galdames Bravo, “On the Norm with Respect to Vector Measures of the Solution of an Infinite System of Ordinary Differential Equations,” Mediterranean Journal of Mathematics, 2014. View at Publisher · View at Google Scholar
  • Umit Cakan, and Ismet Ozdemir, “An Application Of Darbo Fixed- Point Theorem To A Class Of Functional Integral Equations,” Numerical Functional Analysis and Optimization, vol. 36, no. 1, pp. 29–40, 2015. View at Publisher · View at Google Scholar
  • Jianhua Chen, and Xianhua Tang, “Generalizations of Darbo’s fixed point theorem via simulation functions with application to functional integral equations,” Journal of Computational and Applied Mathematics, vol. 296, pp. 564–575, 2016. View at Publisher · View at Google Scholar
  • Ismet Ozdemir, and Umit Cakan, “The Solvability Of Some Nonlinear Functional Integral Equations,” Studia Scientiarum Mathematicarum Hungarica, vol. 53, no. 1, pp. 7–21, 2016. View at Publisher · View at Google Scholar