Open Access
2015 On some new converses of convex inequalities in Hilbert space
Rozarija Jakšić, Josip Pečarić
Banach J. Math. Anal. 9(2): 63-82 (2015). DOI: 10.15352/bjma/09-2-6


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.


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Rozarija Jakšić. Josip Pečarić. "On some new converses of convex inequalities in Hilbert space." Banach J. Math. Anal. 9 (2) 63 - 82, 2015.


Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1325.47036
MathSciNet: MR3296106
Digital Object Identifier: 10.15352/bjma/09-2-6

Primary: 47A63
Secondary: 47A64 , 47C99

Keywords: Convex functions , Jensen's inequality , Lah--Ribari\v{c}'s inequality , means , ‎selfadjoint operators

Rights: Copyright © 2015 Tusi Mathematical Research Group

Vol.9 • No. 2 • 2015
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