Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# On Some Riemann-Stieltjes Integral Inequalities of Generalized Trapezoid Type with Applications

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. Preprints 2018, 2018080453 (doi: 10.20944/preprints201808.0453.v1). Dragomir, S. On Some Riemann-Stieltjes Integral Inequalities of Generalized Trapezoid Type with Applications. Preprints 2018, 2018080453 (doi: 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

MATHEMATICS & COMPUTER SCIENCE, Analysis

## Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Views 0
Downloads 0
Comments 0
Metrics 0

Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.