Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
Ostrowski’s type inequalities; Riemann-Stieltjes integral inequalities; unitary operators in Hilbert spaces; spectral theory; quadrature rules
Ostrowski’s type inequalities; Riemann-Stieltjes integral inequalities; unitary operators in Hilbert spaces; spectral theory; quadrature rules
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.
References:
[1] Dragomir, S. S.: On the Ostrowski’s inequality for Riemann-Stieltjes integral. Korean J. Appl. Math. 7 (2000), 477–485. Zbl 0969.26017
[2] Dragomir, S. S.: On the Ostrowski inequality for Riemann-Stieltjes integral $\int _{a}^{b}f\left( t\right) du\left( t\right) $ where $f$ is of Hölder type and $u$ is of bounded variation and applications. J. KSIAM 5 (1) (2001), 35–45.
[3] Dragomir, S. S.: Ostrowski’s type inequalities for continuous functions of selfadjoint operators on Hilbert spaces: a survey of recent results. Ann. Funct. Anal. 2 (1) (2011), 139–205. DOI 10.15352/afa/1399900269 | MR 2811214 | Zbl 1231.47012
[4] Dragomir, S. S.: Ostrowski’s type inequalities for some classes of continuous functions of selfadjoint operators in Hilbert spaces. Comput. Math. Appl. 62 (12) (2011), 4439–4448. DOI 10.1016/j.camwa.2011.10.020 | MR 2855586 | Zbl 1236.26016
[5] Helmberg, G.: Introduction to Spectral Theory in Hilbert Space. John Wiley and Sons, 1969. MR 0243367 | Zbl 0177.42401
[6] Ostrowski, A.: Über die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert (German). erman), Comment. Math. Helv. 10 (1) (1937), 226–227. DOI 10.1007/BF01214290 | MR 1509574
Search
Partner of
