Advances in Operator Theory

Strengthened converses of the Jensen and Edmundson-Lah-Ribarič inequalities

Mario Krnić, Rozarija Mikić, and Josip Pečarić

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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.

Article information

Source
Adv. Oper. Theory, Volume 1, Number 1 (2016), 104-122.

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

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512416210

Digital Object Identifier
doi:10.22034/aot.1610.1040

Mathematical Reviews number (MathSciNet)
MR3721328

Zentralblatt MATH identifier
06664784

Subjects
Primary: 26D15: Inequalities for sums, series and integrals
Secondary: 47B38: Operators on function spaces (general) 26A51: Convexity, generalizations

Keywords
positive linear functional convex function converse Jensen inequality Edmundson–Lah–Ribarič inequality Hölder inequality Hermite–Hadamard inequality

Citation

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


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