An Application of Krasnoselskii Fixed Point Theorem to Some Nonlinear Functional Integral Equations

Year 2014, , 66 - 73, 03.02.2015

Ümit Çakan İsmet Özdemir

https://doi.org/10.17100/nevbiltek.210931

Cited By: 1

Abstract

The purpose of this paper is to study the existence of solutions of some nonlinear functional integral equations in the space of continuous functions defined on interval  under some conditions. To do this, we will use Krasnoselskii Fixed Point Theorem and Ascoli-Arzela Theorem. Finally we will give an example to illustrate our result.

Keywords

Nonlinear Integral equations, Krasnoselskii Fixed Point Theorem, Ascoli-Arzela Theorem

Krasnoselskii Sabit Nokta Teoreminin Lineer Olmayan Bazı Fonksiyonel İntegral Denklemlere Uygulaması

Abstract

Bu çalışmanın amacı [0, ] aralığı üzerinde tanımlı ve sürekli fonksiyonların uzayında, bazı kabuller altında lineer olmayan bazı fonksiyonel integral denklemlerin çözümlerinin varlığını araştırmaktır. Bunun için Krasnoselskii Sabit Nokta Teoremini ve AscoliArzela Teoremini kullanılacaktır. Son olarak elde edilen sonuçları açıklayıcı bir örnek verilecektir

Keywords

Lineer Olmayan İntegral Denklemler, Krasnoselskii Sabit Nokta Teoremi, Ascoli-Arzela Teoremi

References

• Hu S., Khavanin M. and Zhuang W., “Integral equations arising in the kinetic theory of gases”, Aplpicable Analysis, 34, 261-266, 1989.
• Krasnoselskii M. A., “Topological Methods in the Theory of Nonlinear Integral Equations”, Pergamon Press, New York, 1964.
• Deimling K., “Nonlinear Functional Analysis”, Springer, Berlin, 1985.
• Banaś J. and Martinon A., “Monotonic solutions of a quadratic integral equation of Volterra
• type”, Computers & Mathematics with Applications, 47, 271-279, 2004.
• Özdemir İ., Çakan Ü. and İlhan B., “On the existence of the solutions forsSome nonlinear
• Volterra integral equations”, Abstract and Applied Analysis, 2013, Article ID 689234, 5 pages.
• Krasnoselskii M. A., “Some problems of nonlinear analysis”, American Mathematical Society Translations, Series 2, 10(2), 345-409, 1958.
• Banaś J. and Goebel K., “Measures of Noncompactness in Banach Space, Lecture Notes in Pure
• and Applied Mathematics, Vol. 60”, Dekker, New York, 1980.
• Ma Tsoy-Wo, “Banach-Hilbert Spaces, Vector Measures and Group Representations”, WorldScientific, Singapore, 2002.
• Reed M. and Simon B., “Functional Analysis”, Academic Press, Boston, 1980.