On Kurzweil-Stieltjes integral in a Banach space

Result code in IS VaVaI
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Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On Kurzweil-Stieltjes integral in a Banach space
Original language description
In the paper we deal with the Kurzweil-Stieltjes integration of functions having values in a Banach space $X.$ We extend results obtained by Stefan Schwabik and complete the theory so that it will be well applicable to prove results on the continuous dependence of solutions to generalized linear differential equations in a Banach space. By Schwabik, the integral $int_a^b d[F]g$ exists if $F[a,b]to L(X)$ has a bounded semi-variation on $[a,b]$ and $g [a,b]to X$ is regulated on $[a,b].$ We prove that thisintegral has sense also if $F$ is regulated on $[a,b]$ and $g$ has a bounded semi-variation on $[a,b].$ Furthermore, the integration by parts theorem is presented under the assumptions not covered by Schwabik (2001) and Naralenkov (2004), and the substitution formula is proved.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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