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

Raïssouli, Mustapha; Zine, Rabie

doi:10.1215/20088752-2018-0035

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Cited by 4 publications

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“…with equalities if and only if a = b. For further other means, not needed here, we can consult [22,23] for instance.…”

Section: Introductionmentioning

confidence: 99%

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Further mean inequalities via some integral inequalities

Raïssouli

Chergui²

2021

Filomat

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Recently intensive efforts are deployed to establish inequalities involving some bivariate means. In this paper we aim to investigate further mean inequalities. The approach employed here is based on a combination of the integral representations of the involved means with some advanced integral inequalities known in the literature. In particular, applying the Gr?ss inequality and the Ostrowski inequality we derive a lot of estimations for differences between some standard means and weighted means.

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“…with equalities if and only if a = b. For further other means, not needed here, we can consult [22,23] for instance.…”

Section: Introductionmentioning

confidence: 99%

“…The following integral formulas, that can be found in several references like [22], will be needed in the sequel.…”

Section: Introductionmentioning

confidence: 99%