Tuo-Yeong Lee (2005)
Mathematica Bohemica
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It is shown that a Banach-valued Henstock-Kurzweil integrable function on an -dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function and a continuous function such that for all .
Márcia Federson (2002)
Mathematica Bohemica
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Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains that of Henstock. In the present paper, we consider abstract vector integrals of Kurzweil and...
A. Sikorska-Nowak (2007)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We prove an existence theorem for the equation x' = f(t,xₜ), x(Θ) = φ(Θ), where xₜ(Θ) = x(t+Θ), for -r ≤ Θ < 0, t ∈ Iₐ, Iₐ = [0,a], a ∈ R₊ in a Banach space, using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of the measure of weak noncompactness. ...
Kirill Naralenkov (2011)
Czechoslovak Mathematical Journal
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We make some comments on the problem of how the Henstock-Kurzweil integral extends the McShane integral for vector-valued functions from the descriptive point of view.
Bianca Satco (2006)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper, we prove the existence of continuous solutions of a Volterra integral inclusion involving the Henstock-Kurzweil-Pettis integral. Since this kind of integral is more general than the Bochner, Pettis and Henstock integrals, our result extends many of the results previously obtained in the single-valued setting or in the set-valued case.
L. Di Piazza, K. Musiał (2006)
Studia Mathematica
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We prove that several results of Talagrand proved for the Pettis integral also hold for the Kurzweil-Henstock-Pettis integral. In particular the Kurzweil-Henstock-Pettis integrability can be characterized by cores of the functions and by properties of suitable operators defined by integrands.