Refining and reversing the Hermite–Hadamard inequality for the Fenchel conjugate

Mustapha Raïssouli; Rabie Zine

doi:10.1215/20088752-2018-0035

Abstract

In this paper, we give some refinements and reverses for the Hermite–Hadamard inequality when the integrand map is the Fenchel conjugate in convex analysis. The theoretical results obtained by our present functional approach immediately imply those of an operator version in a simple and elegant way. An application for scalar means is provided as well.

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Mustapha Raïssouli. Rabie Zine. "Refining and reversing the Hermite–Hadamard inequality for the Fenchel conjugate." Ann. Funct. Anal. 10 (3) 357 - 369, August 2019. https://doi.org/10.1215/20088752-2018-0035

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Received: 12 October 2018; Accepted: 25 November 2018; Published: August 2019

First available in Project Euclid: 6 August 2019

zbMATH: 07089123

MathSciNet: MR3989181

Digital Object Identifier: 10.1215/20088752-2018-0035

Subjects:

Primary: 46N10

Secondary: 47A63 , 47A64

Keywords: convex analysis , Fenchel conjugate , Hermite–Hadamard inequality

Abstract

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