The Hermite-Hadamard inequality revisited: Some new proofs and applications

Ilham A. Aliev; Mehmet E. Tamar; Cagla Sekin

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arXiv · 2010.03966

The Hermite-Hadamard inequality revisited: Some new proofs and applications

Ilham A. Aliev·Mehmet E. Tamar·Cagla Sekin

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Abstract

New proofs of the classical Hermite-Hadamard inequality are presented and several applications are given, including Hadamard-type inequalities for the functions, whose derivatives have inflection points or whose derivatives are convex. Morever, some estimates from below and above for the first moments of functions $% f:[a,b]\rightarrow %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion $ about the center point $c=(a+b)/2$ are obtained and the reverse Hardy inequality for convex functions $f:[0,\infty )\rightarrow (0,\infty )$ is established.

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BibTeX RIS

Ilham A. Aliev, Mehmet E. Tamar, Cagla Sekin. 2020-09-22. The Hermite-Hadamard inequality revisited: Some new proofs and applications. https://arxiv.org/abs/2010.03966

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