Some properties of Uryson-Stieltjes integral operators.
Banaś, Józef (1998)
International Journal of Mathematics and Mathematical Sciences
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Banaś, Józef (1998)
International Journal of Mathematics and Mathematical Sciences
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Štefan Schwabik (2001)
Mathematica Bohemica
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Integration by parts results concerning Stieltjes integrals for functions with values in Banach spaces are presented. The background of the theory is the Kurzweil approach to integration based on Riemann type integral sums, which leads to the Perron integral.
Milan Tvrdý (1989)
Časopis pro pěstování matematiky
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Štefan Schwabik, Milan Tvrdý (1973)
Časopis pro pěstování matematiky
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R. Norvaiša (2002)
Studia Mathematica
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The main result is a Young-Stieltjes integral representation of the composition ϕ ∘ f of two functions f and ϕ such that for some α ∈ (0,1], ϕ has a derivative satisfying a Lipschitz condition of order α, and f has bounded p-variation for some p < 1 + α. If given α ∈ (0,1], the p-variation of f is bounded for some p < 2 + α, and ϕ has a second derivative satisfying a Lipschitz condition of order α, then a similar result holds with the Young-Stieltjes integral replaced by its extension. ...