Linear Volterra-Stieltjes integral equations in the sense of the Kurzweil-Henstock integral

Márcia Federson; Ricardo Bianconi

Displaying similar documents to “Linear Volterra-Stieltjes integral equations in the sense of the Kurzweil-Henstock integral”

Substitution formulas for the Kurzweil and Henstock vector integrals

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...

On the Volterra integral equation and the Henstock-Kurzweil integral.

Bugajewski, D. (1998)

Mathematica Pannonica

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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 $(x, y) \in {[0, 1]}^{2}$ .

Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces.

Sikorska-Nowak, Aneta (2007)

Journal of Applied Mathematics

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Volterra integral inclusions via Henstock-Kurzweil-Pettis integral

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.

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.

The origin and developments of Kurzweil's generalized Riemann integral

Jean Mawhin (2025)

Czechoslovak Mathematical Journal

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The paper describes to origin and motivation of Kurzweil in introducing a Riemann-type definition for generalized Perron integrals and his further contributions to the topics.