Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals

A. Sikorska-Nowak

Displaying similar documents to “Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals”

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 $x^{'} (t) = f (t, x (t)), x (0) = x_{0}, t \in I_{α} = [0, α]$ 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.

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.

Characterizations of Kurzweil-Henstock-Pettis integrable functions

L. Di Piazza, K. Musiał (2006)

Studia Mathematica

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We prove that several results of Talagrand proved for the Pettis integral also hold for the Kurzweil-Henstock-Pettis integral. In particular the Kurzweil-Henstock-Pettis integrability can be characterized by cores of the functions and by properties of suitable operators defined by integrands.

On Henstock-Dunford and Henstock-Pettis integrals.

Ye, Guoju, An, Tianqing (2001)

International Journal of Mathematics and Mathematical Sciences

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A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals

C. K. Fong (2002)

Czechoslovak Mathematical Journal

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We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.

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.

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