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Displaying similar documents to “Substitution formulas for the Kurzweil and Henstock vector integrals”

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.

Bounded linear functionals on the space of Henstock-Kurzweil integrable functions

Tuo-Yeong Lee (2009)

Czechoslovak Mathematical Journal

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Applying a simple integration by parts formula for the Henstock-Kurzweil integral, we obtain a simple proof of the Riesz representation theorem for the space of Henstock-Kurzweil integrable functions. Consequently, we give sufficient conditions for the existence and equality of two iterated Henstock-Kurzweil integrals.

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 ( ) ∫ 0 x ( ) ∫ 0 y f ( u , v ) d v d u = ( ) ∫ 0 y ( ) ∫ 0 x f ( u , v ) d u d v = F ( x , y ) for all ( x , y ) ∈ [ 0 , 1 ] 2 .