An extension of the Hermite-Hadamard inequality for a power of a convex function

Sayyari, Yamin; Dehghanian, Mehdi; Park, Choonkil; Paokanta, Siriluk

doi:10.1515/math-2022-0542

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2023

2024

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Cited by 4 publications

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“…Recent advances on the Jensen and Hermite-Hadamard inequalities can be found in [13], and the references therein.…”

Section: Complementsmentioning

confidence: 99%

Exploring nine different proofs of a famous logarithmic inequality

Chesneau

2024

AMCS

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This article explores and analyzes nine different proofs of a fundamental logarithmic inequality, say "log(1+x)/x ≥ 1/ (1+x/2) for x>-1". Some proofs are already published; others are new or consider new approaches or new angles of research. They are based on various techniques, such as differentiation, series expansion, and the application of well-known inequalities such as the primitive, Cauchy-Schwarz, logarithmic mean, hyperbolic tangent function, Jensen, and Hermite-Hadamard inequalities. A graphical work illustrates some results. Therefore, our study clarifies the different mathematical foundations of this seemingly straightforward but important inequality and goes beyond it with some new material.

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“…Recent advances on the Jensen and Hermite-Hadamard inequalities can be found in [13], and the references therein.…”

Section: Complementsmentioning

confidence: 99%