An inequality for the Riemann-Stieltjes integral
Authors:
Richard Darst and Harry Pollard
Journal:
Proc. Amer. Math. Soc. 25 (1970), 912-913
MSC:
Primary 26.46
DOI:
https://doi.org/10.1090/S0002-9939-1970-0260945-3
MathSciNet review:
0260945
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Abstract | References | Similar Articles | Additional Information
Abstract: Let $g$ and $h$ be real valued and continuous on the interval $[a,b]$, and suppose that the variation, $V[h]$, of $h$ on $[a,b]$ is finite. By completely elementary methods, it is shown that $V[h] \cdot {\sup _{_{a \leqq \alpha < \beta \leqq b}}}(g(\beta ) - g(\alpha ))$ is an upper bound for $\int _a^b {(h - \inf h)dg}$.
- Tord Ganelius, Un théorème taubérien pour la transformation de Laplace, C. R. Acad. Sci. Paris 242 (1956), 719–721 (French). MR 74579 ---, An inequality for Stieltjes integrals, Proc. Fourteenth Scandinavian Math. Congress, Copenhagen, 1964.
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
- Rainer Wüst, Beweis eines Lemmas von Ganelius, Jber. Deutsch. Math.-Verein. 71 (1969), no. 1, 229–230. (1 plate) (German). MR 583185
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Keywords:
Riemann-Stieltjes integral,
bounded variation,
upper bound
Article copyright:
© Copyright 1970
American Mathematical Society