Displaying similar documents to “Estimates of the remainder in Taylor’s theorem using the Henstock-Kurzweil integral”

Henstock-Kurzweil and McShane product integration; descriptive definitions

Antonín Slavík, Štefan Schwabik (2008)

Czechoslovak Mathematical Journal

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The Henstock-Kurzweil and McShane product integrals generalize the notion of the Riemann product integral. We study properties of the corresponding indefinite integrals (i.e. product integrals considered as functions of the upper bound of integration). It is shown that the indefinite McShane product integral of a matrix-valued function A is absolutely continuous. As a consequence we obtain that the McShane product integral of A over [ a , b ] exists and is invertible if and only if A is Bochner...

On a generalization of Henstock-Kurzweil integrals

Jan Malý, Kristýna Kuncová (2019)

Mathematica Bohemica

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We study a scale of integrals on the real line motivated by the M C α integral by Ball and Preiss and some recent multidimensional constructions of integral. These integrals are non-absolutely convergent and contain the Henstock-Kurzweil integral. Most of the results are of comparison nature. Further, we show that our indefinite integrals are a.e. approximately differentiable. An example of approximate discontinuity of an indefinite integral is also presented.

A nonexistence result for the Kurzweil integral

Pavel Krejčí, Jaroslav Kurzweil (2002)

Mathematica Bohemica

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It is shown that there exist a continuous function f and a regulated function g defined on the interval [ 0 , 1 ] such that g vanishes everywhere except for a countable set, and the K * -integral of f with respect to g does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions.

The L r Henstock-Kurzweil integral

Paul M. Musial, Yoram Sagher (2004)

Studia Mathematica

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We present a method of integration along the lines of the Henstock-Kurzweil integral. All L r -derivatives are integrable in this method.

A full characterization of multipliers for the strong ρ -integral in the euclidean space

Lee Tuo-Yeong (2004)

Czechoslovak Mathematical Journal

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We study a generalization of the classical Henstock-Kurzweil integral, known as the strong ρ -integral, introduced by Jarník and Kurzweil. Let ( 𝒮 ρ ( E ) , ∥ · ∥ ) be the space of all strongly ρ -integrable functions on a multidimensional compact interval E , equipped with the Alexiewicz norm ∥ · ∥ . We show that each element in the dual space of ( 𝒮 ρ ( E ) , ∥ · ∥ ) can be represented as a strong ρ -integral. Consequently, we prove that f g is strongly ρ -integrable on E for each strongly ρ -integrable function f if and only if g is...