Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces.
Sikorska-Nowak, Aneta (2007)
Journal of Applied Mathematics
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Sikorska-Nowak, Aneta (2007)
Journal of Applied Mathematics
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Sikorska-Nowak, Aneta, Nowak, Grzegorz (2007)
International Journal of Mathematics and Mathematical Sciences
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Bugajewski, D. (1998)
Mathematica Pannonica
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Mieczysław Cichoń, Ireneusz Kubiaczyk, Sikorska-Nowak, Aneta Sikorska-Nowak, Aneta (2004)
Czechoslovak Mathematical Journal
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In this paper we prove an existence theorem for the Cauchy problem using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function satisfies some conditions expressed in terms of measures of weak noncompactness.
Márcia Federson, Ricardo Bianconi (2001)
Archivum Mathematicum
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In 1990, Hönig proved that the linear Volterra integral equation where the functions are Banach space-valued and is a Kurzweil integrable function defined on a compact interval of the real line , admits one and only one solution in the space of the Kurzweil integrable functions with resolvent given by the Neumann series. In the present paper, we extend Hönig’s result to the linear Volterra-Stieltjes integral equation in a real-valued context.
Afif Ben Amar (2011)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we examine the set of weakly continuous solutions for a Volterra integral equation in Henstock-Kurzweil-Pettis integrability settings. Our result extends those obtained in several kinds of integrability settings. Besides, we prove some new fixed point theorems for function spaces relative to the weak topology which are basic in our considerations and comprise the theory of differential and integral equations in Banach spaces.
Satco, Bianca (2009)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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