0385118 - MÚ 2013 RIV CZ eng J - Journal Article
Monteiro, G.A. - Tvrdý, Milan
On Kurzweil-Stieltjes integral in a Banach space.
Mathematica Bohemica. Roč. 137, č. 4 (2012), s. 365-381. ISSN 0862-7959
Institutional research plan: CEZ:AV0Z10190503
Institutional support: RVO:67985840
Keywords : Kurzweil-Stielthes integral * substitution formula * integration-by-parts
Subject RIV: BA - General Mathematics
http://www.dml.cz/handle/10338.dmlcz/142992

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 this integral 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.
Permanent Link: http://hdl.handle.net/11104/0214499