New proofs of Fejer's and discrete Hermite-Hadamard inequalities with applications

Year 2023, Volume: 72 Issue: 4, 1110 - 1125, 29.12.2023

Çağla Sekin , Mehmet Emin Tamar , İlham Aliyev

https://doi.org/10.31801/cfsuasmas.1262668

Abstract

New proofs of the classical Fejer inequality and discrete Hermite-Hadamard inequality (HH) are presented and several applications are given, including (HH)-type inequalities for the functions, whose derivatives have inflection points. Morever, some estimates from below and above for the first moments of functions $f:[a,b]\rightarrow \mathbb{R}$ about the midpoint $c=(a+b)/2$ are obtained and the reverse Hardy inequality for convex functions $f:(0,\infty )\rightarrow (0,\infty )$ is established.

Keywords

Fejer inequality, convex functions, discrete Hermite-Hadamard inequality, Jensen inequality, Hardy inequality

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