Some Weighted Inequalities for Riemann–Stieltjes Integral When a Function Is Bounded

  • Silvestru Sever DragomirEmail author
Part of the Springer Optimization and Its Applications book series (SOIA, volume 151)


In this chapter we provide some simple ways to approximate the Riemann–Stieltjes integral of a product of two functions \(\int _{a}^{b}f\left ( t\right ) g\left ( t\right ) dv\left ( t\right )\) by the use of simpler quantities and under several assumptions for the functions involved, one of them satisfying the boundedness condition
$$\displaystyle \left \vert f\left ( t\right ) -\frac {\gamma +\Gamma }{2}\right \vert \leq \frac { 1}{2}\left \vert \Gamma -\gamma \right \vert \ \text{for each}\ t\in \left [ a,b \right ] , $$
where \(f:\left [ a,b\right ] \rightarrow \mathbb {C}\). Applications for continuous functions of selfadjoint operators and functions of unitary operators on Hilbert spaces are also given.

1991 Mathematics Subject Classification

26D15 26D10 26D07 26A33 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Mathematics College of Engineering and ScienceVictoria UniversityMelbourneAustralia
  2. 2.DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences, School of Computer Science and Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa

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