Banach Journal of Mathematical Analysis

On a Jensen-Mercer operator inequality

A. Ivelic, A. Matkovic, and J. E. Pecaric

Full-text: Open access

Abstract

A general formulation of the Jensen-Mercer operator inequality for operator convex functions, continuous fields of operators and unital fields of positive linear mappings is given. As consequences, a global upper bound for Jensen's operator functional and some properties of the quasi-arithmetic operator means and quasi-arithmetic operator means of Mercer's type are obtained.

Article information

Source
Banach J. Math. Anal., Volume 5, Number 1 (2011), 19-28.

Dates
First available in Project Euclid: 14 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1313362976

Digital Object Identifier
doi:10.15352/bjma/1313362976

Mathematical Reviews number (MathSciNet)
MR2738516

Zentralblatt MATH identifier
1221.47031

Subjects
Primary: 47A63: Operator inequalities
Secondary: 47A64: Operator means, shorted operators, etc.

Keywords
Jensen--Mercer operator inequality operator convex functions continuous fields of operators Jensen's operator functional quasi-arithmetic operator means

Citation

Ivelic, A.; Matkovic, A.; Pecaric, J. E. On a Jensen-Mercer operator inequality. Banach J. Math. Anal. 5 (2011), no. 1, 19--28. doi:10.15352/bjma/1313362976. https://projecteuclid.org/euclid.bjma/1313362976


Export citation

References

  • B. Gavrea, J. Jakšetić and J. Pečarić, On a global upper bound for Jessen's inequality, ANZIAM J. 50 (2008), no. 2, 246–257.
  • F. Hansen and G.K. Pedersen, Jensen's operator inequality, Bull. London Math. Soc. 35 (2003), no. 4, 553–564.
  • F. Hansen, J. Pečarić and I. Perić, Jensen's operator inequality and its converses, Math. Scand. 100 (2007), no. 1, 61–73.
  • A. Matković and J. Pečarić, A variant of Jensen's inequality for convex functions of several variables, J. Math. Ineq. 1 (2007), no. 1, 45–51.
  • A. Matković, J. Pečarić and I. Perić, A variant of Jensen's inequality of Mercer's type for operators with applications, Linear Algebra Appl. 418 (2006), no. 2-3, 551–564.
  • A. Matković, J. Pečarić and I. Perić, Refinements of Jensen's inequality of Mercer's type for operator convex functions, Math. Inequal. Appl. 11(1) (2008), 113–126.
  • A. McD. Mercer, A variant of Jensen's inequality, J. Inequal. Pure and Appl. Math. 4 (2003), no. 4, Article 73, 2 pp.
  • S. Simic, On a global upper bound for Jensen's inequality, J. Math. Anal. Appl. 343 (2008), no. 1, 414–419.