Version 1
: Received: 4 September 2018 / Approved: 4 September 2018 / Online: 4 September 2018 (08:20:50 CEST)
How to cite:
Dragomir, S. General Three Points Inequalities for Weighted Riemann-Stieltjes Integral. Preprints2018, 2018090060. https://doi.org/10.20944/preprints201809.0060.v1
Dragomir, S. General Three Points Inequalities for Weighted Riemann-Stieltjes Integral. Preprints 2018, 2018090060. https://doi.org/10.20944/preprints201809.0060.v1
Dragomir, S. General Three Points Inequalities for Weighted Riemann-Stieltjes Integral. Preprints2018, 2018090060. https://doi.org/10.20944/preprints201809.0060.v1
APA Style
Dragomir, S. (2018). General Three Points Inequalities for Weighted Riemann-Stieltjes Integral. Preprints. https://doi.org/10.20944/preprints201809.0060.v1
Chicago/Turabian Style
Dragomir, S. 2018 "General Three Points Inequalities for Weighted Riemann-Stieltjes Integral" Preprints. https://doi.org/10.20944/preprints201809.0060.v1
Abstract
In this paper we provide amongst others some simple error bounds in approximating the weighted Riemann-Stieltjes integral $\int_{a}^{b}f\left(t\right) g\left(t\right) dv\left(t\right) $ by the use of three points formula \begin{equation*} f\left(b\right) \int_{c}^{b}g\left(s\right) dv\left(s\right) +f\left(a\right) \int_{a}^{d}g\left( s\right) dv\left( s\right) -f\left(x\right) \int_{c}^{d}g\left(t\right) dv\left(t\right) \end{equation*} where $x,$ $c,$ $d\in \left[a,b\right],$ $g,$ $v:\left[a,b\right] \rightarrow \mathbb{C}$ under bounded variation and Lipschitzian assumptions for the function $f$ and such that the involved Riemann-Stieltjes integrals exist.
Keywords
Riemann-Stieltjes integral; continuous functions; functions of bounded variation; Lipschitzian functions
Subject
Computer Science and Mathematics, Analysis
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
