Error bounds in approximating the Riemann–Stieltjes integral of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>-class integrands and nonsmooth integrators

Dragomir, Sever S; Harley, C.; Momoniat, E.

doi:10.1016/j.amc.2014.10.022

Applied Mathematics and Computation

2014

DOI: 10.1016/j.amc.2014.10.022

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Error bounds in approximating the Riemann–Stieltjes integral of Cn+1-class integrands and nonsmooth integrators

Sever S Dragomir¹,

C. Harley²,

E. Momoniat³

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2024

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On the Continuous Composition of Integrable Functions

Parsian

2024

Turkish Journal of Mathematics and Computer Science

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‎\begin{abstract}‎ ‎We prove if $\alpha$ be a function of bounded variation on $[a,b]$‎, ‎$[m_{i}‎, ‎M_{i}] \subset \mathbb{R}$ be a closed interval for $1\leq i \leq n$‎, ‎$f_{i}:[a,b]\to [m_{i}‎, ‎M_{i}]$ be Riemann-Stieltjes integrable with respect to $\alpha$‎, ‎and $G‎: ‎\Pi_{i=1}^{i=n} [m_{i},M_{i}] \to \mathbb{R}$ be continuous‎, ‎then $H=G\circ(f_{1}‎, ‎\dots‎ ,‎f_{n})$ is Riemann-Stieltjes integrable with respect to $\alpha$‎. ‎Some another consequences‎, ‎applications and counterexamples are also provided‎. ‎\end{abstract}‎

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On the Continuous Composition of Integrable Functions

Parsian

2024

Turkish Journal of Mathematics and Computer Science

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show abstract

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Error bounds in approximating the Riemann–Stieltjes integral of Cn+1-class integrands and nonsmooth integrators

Cited by 1 publication

References 29 publications

On the Continuous Composition of Integrable Functions

On the Continuous Composition of Integrable Functions

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