Banach Journal of Mathematical Analysis

On some new converses of convex inequalities in Hilbert space

Rozarija Jakšić and Josip Pečarić

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Abstract

In this paper we study some new converses of the operator version for the Jensen inequality and the scalar Lah--Ribarič inequality for continuous convex functions and we will give applications of those results to quasi-arithmetic means and power means for selfadjoint operators. Furthermore, we will also give improvements of the obtained results.

Article information

Source
Banach J. Math. Anal., Volume 9, Number 2 (2015), 63-82.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1419001105

Digital Object Identifier
doi:10.15352/bjma/09-2-6

Mathematical Reviews number (MathSciNet)
MR3296106

Zentralblatt MATH identifier
1325.47036

Subjects
Primary: 47A63: Operator inequalities
Secondary: 47A64: Operator means, shorted operators, etc. 47C99: None of the above, but in this section

Keywords
Selfadjoint operators Jensen's inequality Lah--Ribari\v{c}'s inequality convex functions means

Citation

Jakšić, Rozarija; Pečarić, Josip. On some new converses of convex inequalities in Hilbert space. Banach J. Math. Anal. 9 (2015), no. 2, 63--82. doi:10.15352/bjma/09-2-6. https://projecteuclid.org/euclid.bjma/1419001105


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References

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