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

Silvestru Sever Dragomir ()
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Silvestru Sever Dragomir: Victoria University

A chapter in Differential and Integral Inequalities, 2019, pp 311-339 from Springer

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

Keywords: 26D15; 26D10; 26D07; 26A33 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-27407-8_8

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DOI: 10.1007/978-3-030-27407-8_8

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