Annals of Functional Analysis

New Grüss Type Inequalities for Riemann--Stieltjes Integral With Monotonic Integrators and Applications

Mohammad W. Alomari and Sever S. Dragomir

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper several new inequalities of Grüss' type for Riemann--Stieltjes integral with monotonic nondecreasing integrators under various assumptions for integrands are proved. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well.

Article information

Source
Ann. Funct. Anal., Volume 5, Number 1 (2014), 77-93.

Dates
First available in Project Euclid: 5 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1391614572

Digital Object Identifier
doi:10.15352/afa/1391614572

Mathematical Reviews number (MathSciNet)
MR3119115

Zentralblatt MATH identifier
1288.26012

Subjects
Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 26D15: Inequalities for sums, series and integrals 47A63: Operator inequalities

Keywords
Grüss inequality functions of bounded variation Hölder continuous functions Riemann--Stieltjes integral selfadjoint operators functions of selfadjoint operators

Citation

Alomari, Mohammad W.; Dragomir, Sever S. New Grüss Type Inequalities for Riemann--Stieltjes Integral With Monotonic Integrators and Applications. Ann. Funct. Anal. 5 (2014), no. 1, 77--93. doi:10.15352/afa/1391614572. https://projecteuclid.org/euclid.afa/1391614572


Export citation

References

  • M.W. Alomari and S.S. Dragomir, New Grüss type inequalities for the Stieltjes integral with applications, submitted. Avalibale at [http://ajmaa.org/RGMIA/papers/v15/v15a.pdf].
  • G.A. Anastassiou, Grüss type inequalities for the Stieltjes integral, Nonlinear Funct. Anal. Appl. 12 (2007), no. 4, 583–593.
  • G.A. Anastassiou, Chebyshev-Grüss type and comparison of integral means inequalities for the Stieltjes integral, Panamer. Math. J. 17 (2007), no. 3, 91–109.
  • P. Cerone and S.S. Dragomir, New bounds for the Čebyš ev functional, Appl. Math. Lett. 18 (2005) 603–611.
  • P. Cerone and S.S. Dragomir, A refinement of the Grüss inequality and applications, Tamkang J. Math. 38 (2007), no. 1, 37–49.
  • S.S. Dragomir, Inequalities of Grüss type for the Stieltjes integral and applications, Kragujevac J. Math. 26 (2004) 89–112.
  • S.S. Dragomir, New Grüss' type inequalities for functions of bounded variation and applications, Appl. Math. Lett. 25 (2012), no. 10, p. 1475–1479.
  • S.S. Dragomir, New estimates of the Čebyšev functional for Stieltjes integrals and applications, J. Korean Math. Soc. 41 (2004), no. 2, 249–264.
  • S.S. Dragomir, Sharp bounds of Čebyšev functional for Stieltjes integrals and applications, Bull. Austral. Math. Soc. 67 (2003), no. 2, 257–266.
  • S.S. Dragomir, Some integral inequality of Grüss type, Indian J. Pure Appl. Math. 31 (2000), no. 4, 397–415.
  • S.S. Dragomir, Grüss type integral inequality for mappings of $r$-Hölder type and applications for trapezoid formula, Tamkang J. Math. 31 (2000), no. 1, 43–47.
  • S.S. Dragomir, Čebyšev's type inequalities for functions of selfadjoint operators in Hilbert spaces, Linear Multilinear Algebra 58 (2010), no. 7, 805-814.
  • S.S. Dragomir, Grüss' type inequalities for functions of selfadjoint operators in Hilbert spaces, Preprint RGMIA Res. Rep. Coll. 11(e) (2008), Art. 11.
  • S.S. Dragomir, Some new Grüss' type inequalities for functions of selfadjoint operators in Hilbert spaces, Sarajevo J. Math. 18 (2010), 89–107.
  • S.S. Dragomir, Inequalities for the Čebyšev functional of two functions of selfadjoint operators in Hilbert spaces, Aust. J. Math. Anal. Appl. 6 (2009), No. 1, Art 7.
  • S.S. Dragomir, Some inequalities for the Čebyšev functional of two functions of selfadjoint operators in Hilbert spaces, RGMIA Res. Rep. Coll. 11(e) (2008), Art. 8.
  • S.S. Dragomir, Quasi Grüss' type inequalities for continuous functions of selfadjoint operators in Hilbert spaces, Preprint RGMIA Res. Rep. Coll. 13 (2010), Sup. Art. 12.
  • S.S. Dragomir, Grüss' type inequalities for some classes of continuous functions of selfadjoint operators in Hilbert spaces, Preprint RGMIA Res. Rep. Coll. 13 (2010), no. 2, Art. 15.
  • S.S. Dragomir, Operator Inequalities of the Jensen, Čebyšev and Grüss Type. Springer Briefs in Mathematics. Springer, New York, 2012.
  • S.S. Dragomir and I. Fedotov, An inequality of Grüss type for Riemann–Stieltjes integral and applications for special means, Tamkang J. Math. 29 (1998), no. 4, 287–292.
  • G. Grüss, Über das maximum des absoluten Betrages von $ \frac{1}{{b-a}}\int_{a}^{b}{f\left( x\right) g\left( x\right) dx}-\frac{1}{{ \left( {b-a}\right) ^{2}}}\int_{a}^{b}{f\left( x\right) dx}\cdot \int_{a}^{b} {g\left( x\right) dx}$, Math. Z. 39 (1935), 215–226.
  • G. Helmberg, Introduction to Spectral Theory in Hilbert Space, John Wiley & Sons, Inc. -New York, 1969.
  • Z. Liu, Refinement of an inequality of Grüss type for Riemann–Stieltjes integral, Soochow J. Math. 30 (2004), no. 4, 483–489.