Skip to main content


  • Research Article
  • Open Access

On a fixed point theorem of Krasnosel'skii type and application to integral equations

Fixed Point Theory and Applications20062006:30847

  • Received: 15 April 2006
  • Accepted: 13 August 2006
  • Published:


This paper presents a remark on a fixed point theorem of Krasnosel'skii type. This result is applied to prove the existence of asymptotically stable solutions of nonlinear integral equations.


  • Integral Equation
  • Point Theorem
  • Differential Geometry
  • Stable Solution
  • Computational Biology


Authors’ Affiliations

Department of Natural Science, Nha Trang Educational College, 01 Nguyen Chanh Street, Nha Trang City, Vietnam
Department of Mathematics and Computer Science, University of Natural Science, Vietnam National University, 227 Nguyen Van Cu Street, Dist. 5, Ho Chi Minh, Vietnam


  1. Avramescu C: Some remarks on a fixed point theorem of Krasnosel'skii. Electronic Journal of Qualitative Theory of Differential Equations 2003,2003(5):1–15.MathSciNetGoogle Scholar
  2. Avramescu C, Vladimirescu C: Asymptotic stability results for certain integral equations. Electronic Journal of Differential Equations 2005,2005(126):1–10.MathSciNetView ArticleMATHGoogle Scholar
  3. Burton TA: A fixed-point theorem of Krasnosel'skii. Applied Mathematics Letters 1998,11(1):85–88. 10.1016/S0893-9659(97)00138-9MathSciNetView ArticleMATHGoogle Scholar
  4. Burton TA, Kirk C: A fixed point theorem of Krasnosel'skii-Schaefer type. Mathematische Nachrichten 1998, 189: 23–31. 10.1002/mana.19981890103MathSciNetView ArticleMATHGoogle Scholar
  5. Dieudonné J: Foundations of Modern Analysis. Academic Press, New York; 1969:xviii+387.Google Scholar
  6. Hoa LH, Schmitt K: Fixed point theorems of Krasnosel'skii type in locally convex spaces and applications to integral equations. Results in Mathematics 1994,25(3–4):290–314.View ArticleMathSciNetMATHGoogle Scholar
  7. Hoa LH, Schmitt K: Periodic solutions of functional-differential equations of retarded and neutral types in Banach spaces. In Boundary Value Problems for Functional-Differential Equations. Edited by: Henderson J. World Scientific, New Jersey; 1995:177–185.View ArticleGoogle Scholar
  8. Krasnosel'skii MA: Topological Methods in The Theory of Nonlinear Integral Equations. Pergamon Press, New York; 1964:xi + 395.Google Scholar
  9. Zeidler E: Nonlinear Functional Analysis and Its Applications. I. Springer, New York; 1986:xxi+897.View ArticleGoogle Scholar


© L. T. P. Ngoc and N. T. Long. 2006

This article is published under license to BioMed Central Ltd. 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.