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2015 Trapezoidal Type Inequalities for Riemann-Stieltjes Integral Via Čebyšev Functional with Applications
Silvestru Sever Dragomir
Nihonkai Math. J. 26(1): 47-69 (2015).

Abstract

Some new inequalities for the functional \begin{align*} & E_{T}\left( f,u\right) \\ & :=f\left( b\right) \left( u\left( b\right) -\frac{1}{b-a}% \int_{a}^{b}u\left( t\right) dt\right) +f\left( a\right) \left( \frac{1}{b-a}% \int_{a}^{b}u\left( t\right) dt-u\left( a\right) \right) \\ & -\int_{a}^{b}f\left( t\right) du\left( t\right) , \end{align*} under various assumptions for the functions $f$ and $u$ are given. Applications for functions of selfadjoint operators and unitary operators on complex Hilbert spaces are also provided.

Citation

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Silvestru Sever Dragomir. "Trapezoidal Type Inequalities for Riemann-Stieltjes Integral Via Čebyšev Functional with Applications." Nihonkai Math. J. 26 (1) 47 - 69, 2015.

Information

Published: 2015
First available in Project Euclid: 30 March 2016

zbMATH: 1339.26049
MathSciNet: MR3482757

Subjects:
Primary: 26D10, 26D15
Secondary: 47A63

Rights: Copyright © 2015 Niigata University, Department of Mathematics

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Vol.26 • No. 1 • 2015
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