Advances in Operator Theory
- Adv. Oper. Theory
- Volume 1, Number 1 (2016), 104-122.
Strengthened converses of the Jensen and Edmundson-Lah-Ribarič inequalities
In this paper, we give converses of the Jensen and Edmundson-Lah-Ribarič inequalities which are more accurate than the existing ones. These converses are given in a difference form and they rely on the recent refinement of the Jensen inequality obtained via linear interpolation of a convex function. As an application, we also derive improved converse relations for generalized means, for the Hölder and Hermite-Hadamard inequalities as well as for the inequalities of Giaccardi and Petrović.
Adv. Oper. Theory, Volume 1, Number 1 (2016), 104-122.
Received: 28 October 2016
Accepted: 18 November 2016
First available in Project Euclid: 4 December 2017
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Krnić, Mario; Mikić, Rozarija; Pečarić, Josip. Strengthened converses of the Jensen and Edmundson-Lah-Ribarič inequalities. Adv. Oper. Theory 1 (2016), no. 1, 104--122. doi:10.22034/aot.1610.1040. https://projecteuclid.org/euclid.aot/1512416210