| Title:
|
Ostrowski’s type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces (English) |
| Author:
|
Dragomir, S.S. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
233-254 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Ostrowski’s type inequalities |
| Keyword:
|
Riemann-Stieltjes integral inequalities |
| Keyword:
|
unitary operators in Hilbert spaces |
| Keyword:
|
spectral theory |
| Keyword:
|
quadrature rules |
| MSC:
|
26D15 |
| MSC:
|
41A51 |
| MSC:
|
47A63 |
| idZBL:
|
Zbl 06537727 |
| idMR:
|
MR3434605 |
| DOI:
|
10.5817/AM2015-4-233 |
| . |
| Date available:
|
2015-11-30T10:01:30Z |
| Last updated:
|
2016-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144482 |
| . |
| Reference:
|
[1] Dragomir, S. S.: On the Ostrowski’s inequality for Riemann-Stieltjes integral.Korean J. Appl. Math. 7 (2000), 477–485. Zbl 0969.26017 |
| Reference:
|
[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. |
| Reference:
|
[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. Zbl 1231.47012, MR 2811214, 10.15352/afa/1399900269 |
| Reference:
|
[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. Zbl 1236.26016, MR 2855586, 10.1016/j.camwa.2011.10.020 |
| Reference:
|
[5] Helmberg, G.: Introduction to Spectral Theory in Hilbert Space.John Wiley and Sons, 1969. Zbl 0177.42401, MR 0243367 |
| Reference:
|
[6] Ostrowski, A.: Über die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert (German).erman), Comment. Math. Helv. 10 (1) (1937), 226–227. MR 1509574, 10.1007/BF01214290 |
| . |
