On a generalization of the Perron integral on one-dimensional intervals

Jaroslav Kurzweil; Jiři Jarník

Displaying similar documents to “On a generalization of the Perron integral on one-dimensional intervals”

Ninety years of Jaroslav Kurzweil

Jiří Jarník, Pavel Krejčí, Antonín Slavík, Milan Tvrdý, Ivo Vrkoč (2016)

Mathematica Bohemica

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Differential equations in banach space and henstock-kurzweil integrals

Ireneusz Kubiaczyk, Aneta Sikorska (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, using the properties of the Henstock-Kurzweil integral and corresponding theorems, we prove the existence theorem for the equation x' = f(t,x) and inclusion x' ∈ F(t,x) in a Banach space, where f is Henstock-Kurzweil integrable and satisfies some conditions.

Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion

Tuo-Yeong Lee (2005)

Mathematica Bohemica

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It is shown that a Banach-valued Henstock-Kurzweil integrable function on an $m$ -dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function $f {[0, 1]}^{2} ⟶ ℝ$ and a continuous function $F {[0, 1]}^{2} ⟶ ℝ$ such that $(¶) \int_{0}^{x} \{(¶) \int_{0}^{y} f (u, v) d v\} d u = (¶) \int_{0}^{y} \{(¶) \int_{0}^{x} f (u, v) d u\} d v = F (x, y)$ for all $(x, y) \in {[0, 1]}^{2}$ .

Some characterizations of the primitive of strong Henstock-Kurzweil integrable functions

Guoju Ye (2006)

Mathematica Bohemica

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In this paper we give some complete characterizations of the primitive of strongly Henstock-Kurzweil integrable functions which are defined on $ℝ^{m}$ with values in a Banach space.