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

摘要

Some Ostrowski’s type inequalities for the Riemann-Stieltjes integral $int _{a}^{b}fleft( e^{it}ight) duleft( tight) $ of continuous complex valued integrands $fcolon mathcal{C}left( 0,1ight) ightarrow mathbb{C}$ defined on the complex unit circle $mathcal{C}left( 0,1ight) $ and various subclasses of integrators $ucolon left[ a,bight] subseteq left[ 0,2pi ight] ightarrow mathbb{C}$ of bounded variation are given. Natural applications for functions of unitary operators in Hilbert spaces are provided as well.