Version 1
: Received: 21 August 2018 / Approved: 27 August 2018 / Online: 27 August 2018 (11:06:59 CEST)
How to cite:
Dragomir, S. On Some Riemann-Stieltjes Integral Inequalities of Generalized Trapezoid Type with Applications. Preprints2018, 2018080453. https://doi.org/10.20944/preprints201808.0453.v1
Dragomir, S. On Some Riemann-Stieltjes Integral Inequalities of Generalized Trapezoid Type with Applications. Preprints 2018, 2018080453. https://doi.org/10.20944/preprints201808.0453.v1
Dragomir, S. On Some Riemann-Stieltjes Integral Inequalities of Generalized Trapezoid Type with Applications. Preprints2018, 2018080453. https://doi.org/10.20944/preprints201808.0453.v1
APA Style
Dragomir, S. (2018). On Some Riemann-Stieltjes Integral Inequalities of Generalized Trapezoid Type with Applications. Preprints. https://doi.org/10.20944/preprints201808.0453.v1
Chicago/Turabian Style
Dragomir, S. 2018 "On Some Riemann-Stieltjes Integral Inequalities of Generalized Trapezoid Type with Applications" Preprints. https://doi.org/10.20944/preprints201808.0453.v1
Abstract
In this paper we provide some bounds for the error in approximating the Riemann-Stieltjes integral $\int_{a}^{b}f (t) du (t)$ by the generalized trapezoidal rule \begin{equation*} \left[ u\left( b\right) -u\left( x\right) \right] f\left( b\right) +\left[ u\left( x\right) -u\left( a\right) \right] f\left( a\right) \end{equation*} under various assumptions for the integrand $f$ and the integrator $u$ for which the above integral exists. Applications for continuous functions of selfadjoint operators and unitary operators in Hilbert spaces are provided as well.
Keywords
Riemann-Stieltjes integral, Trapezoidal Quadrature Rule, Selfadjoint operators, Functions of Selfadjoint operators, Spectral representation, Inequalities for selfadjoint operators
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.
