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Autumn 2016 Strengthened converses of the Jensen and Edmundson-Lah-Ribarič inequalities
Mario Krnić, Rozarija Mikić, Josip Pečarić
Adv. Oper. Theory 1(1): 104-122 (Autumn 2016). DOI: 10.22034/aot.1610.1040

Abstract

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.

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Mario Krnić. Rozarija Mikić. Josip Pečarić. "Strengthened converses of the Jensen and Edmundson-Lah-Ribarič inequalities." Adv. Oper. Theory 1 (1) 104 - 122, Autumn 2016. https://doi.org/10.22034/aot.1610.1040

Information

Received: 28 October 2016; Accepted: 18 November 2016; Published: Autumn 2016
First available in Project Euclid: 4 December 2017

zbMATH: 06664784
MathSciNet: MR3721328
Digital Object Identifier: 10.22034/aot.1610.1040

Subjects:
Primary: 26D15
Secondary: 26A51‎ , 47B38

Keywords: converse , convex function , Edmundson–Lah–Ribarič inequality , Hermite–Hadamard inequality , Hölder inequality , Jensen inequality , Positive linear functional

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.1 • No. 1 • Autumn 2016
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