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

摘要

summary: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.