Displaying similar documents to “Controlled convergence theorems for Henstock-Kurzweil-Pettis integral on m -dimensional compact intervals”

Some results about the Henstock-Kurzweil Fourier transform

Francisco J. Mendoza Torres, Juan A. Escamilla Reyna, Salvador Sánchez Perales (2009)

Mathematica Bohemica

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We consider the Fourier transform in the space of Henstock-Kurzweil integrable functions. We prove that the classical results related to the Riemann-Lebesgue lemma, existence and continuity are true in appropriate subspaces.

The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem

Mieczysław Cichoń, Ireneusz Kubiaczyk, Sikorska-Nowak, Aneta Sikorska-Nowak, Aneta (2004)

Czechoslovak Mathematical Journal

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In this paper we prove an existence theorem for the Cauchy problem x ' ( t ) = f ( t , x ( t ) ) , x ( 0 ) = x 0 , t ∈ I α = [ 0 , α ] 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 measures of weak noncompactness.

A step to Kurzweil-Henstock—an outline

B. D. Craven (2004)

Mathematica Bohemica

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A short approach to the Kurzweil-Henstock integral is outlined, based on approximating a real function on a compact interval by suitable step-functions, and using filterbase convergence to define the integral. The properties of the integral are then easy to establish.

A scalar Volterra derivative for the PoU-integral

V. Marraffa (2005)

Mathematica Bohemica

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A weak form of the Henstock Lemma for the P o U -integrable functions is given. This allows to prove the existence of a scalar Volterra derivative for the P o U -integral. Also the P o U -integrable functions are characterized by means of Pettis integrability and a condition involving finite pseudopartitions.