A generalization of Darbo’s theorem with application to the solvability of systems of integral equations

A generalization of Darbo’s theorem with application to the solvability of systems of integral equations

In this paper, we give an extension of Darbo’s fixed point theorem associated with measures of noncompactness, and present some results on the existence of coupled fixed points for a class of condensing operators in Banach spaces. Moreover, as an application, we study the problem of existence of sol...

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Veröffentlicht in:Journal of computational and applied mathematics 2014-04, Vol.260, p.68-77
Hauptverfasser: Aghajani, A., Allahyari, R., Mursaleen, M.
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Condensing
Coupled fixed point
Integral equations
Joining
Mathematical models
Measure of noncompactness
Modulus of continuity
Nonlinearity
Operators (mathematics)
System of integral equations
Theorems
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Beschreibung
Zusammenfassung:In this paper, we give an extension of Darbo’s fixed point theorem associated with measures of noncompactness, and present some results on the existence of coupled fixed points for a class of condensing operators in Banach spaces. Moreover, as an application, we study the problem of existence of solutions for a general system of nonlinear integral equations.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2013.09.039