On a fixed point theorem of Krasnosel'skii type and application to integral equations
© L. T. P. Ngoc and N. T. Long. 2006
Received: 15 April 2006
Accepted: 13 August 2006
Published: 9 November 2006
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.
- 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
- Avramescu C, Vladimirescu C: Asymptotic stability results for certain integral equations. Electronic Journal of Differential Equations 2005,2005(126):1–10.MathSciNetView ArticleMATHGoogle Scholar
- 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
- 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
- Dieudonné J: Foundations of Modern Analysis. Academic Press, New York; 1969:xviii+387.Google Scholar
- 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
- 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
- Krasnosel'skii MA: Topological Methods in The Theory of Nonlinear Integral Equations. Pergamon Press, New York; 1964:xi + 395.Google Scholar
- Zeidler E: Nonlinear Functional Analysis and Its Applications. I. Springer, New York; 1986:xxi+897.View ArticleGoogle Scholar
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