Kneser-type theorem for the Darboux problem in Banach spaces

Mieczysław Cichoń; Ireneusz Kubiaczyk

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 2, page 267-279
  • ISSN: 0010-2628

Abstract

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In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.

How to cite

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Cichoń, Mieczysław, and Kubiaczyk, Ireneusz. "Kneser-type theorem for the Darboux problem in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 42.2 (2001): 267-279. <http://eudml.org/doc/248780>.

@article{Cichoń2001,
abstract = {In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.},
author = {Cichoń, Mieczysław, Kubiaczyk, Ireneusz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Pettis integral; Fubini theorem; Darboux problem; measure of weak noncompactness; Pettis integral; Fubini theorem; Darboux problem; measure of weak noncompactness},
language = {eng},
number = {2},
pages = {267-279},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Kneser-type theorem for the Darboux problem in Banach spaces},
url = {http://eudml.org/doc/248780},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Cichoń, Mieczysław
AU - Kubiaczyk, Ireneusz
TI - Kneser-type theorem for the Darboux problem in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 2
SP - 267
EP - 279
AB - In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.
LA - eng
KW - Pettis integral; Fubini theorem; Darboux problem; measure of weak noncompactness; Pettis integral; Fubini theorem; Darboux problem; measure of weak noncompactness
UR - http://eudml.org/doc/248780
ER -

References

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