Ostrowski’s type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces

S.S. Dragomir

Address: Mathematics, College of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa

E-mail: sever.dragomir@vu.edu.au

Abstract: Some Ostrowski’s type inequalities for the Riemann-Stieltjes integral $\int _{a}^{b}f\left( e^{it}\right) du\left( t\right) $ of continuous complex valued integrands $f\colon \mathcal{C}\left( 0,1\right) \rightarrow \mathbb{C}$ defined on the complex unit circle $\mathcal{C}\left( 0,1\right) $ and various subclasses of integrators $u\colon \left[ a,b\right] \subseteq \left[ 0,2\pi \right] \rightarrow \mathbb{C}$ of bounded variation are given. Natural applications for functions of unitary operators in Hilbert spaces are provided as well.

AMSclassification: primary 41A51; secondary 26D15, 47A63.

Keywords: Ostrowski’s type inequalities, Riemann-Stieltjes integral inequalities, unitary operators in Hilbert spaces, spectral theory, quadrature rules.

DOI: 10.5817/AM2015-4-233