更細緻的Hermite-Hadamard不等式

Refinements of Hermite-Hadamard inequality

周靜華(Ching-Hua Chou)

指導教授 ： 楊國勝

淡江大學/理學院/數學學系碩士在職專班/碩士(2022年)

https://doi.org/10.6846/TKU.2022.00600

摘要

若 為凸函數， ，則

恆成立，這就是著名的Hermite-Hadamard雙邊不等式，要探
討的是，若 在 中的凸函數，則是否存在兩實數 及
使得下列不等式能成立：

本論文研究的主要目的是要對上式提供一些解。

關鍵字

Hermite-Hadamard不等式 ； 凸函數

並列摘要

If is convex on , then

is known in the literature the Hermite-Hadamard inequality.
There is the question that if is a convex function on
do there exist real numbers and such that

The major goal of this study is to give some answers to the question.

並列關鍵字

Hermite-Hadamard inequality ； convex functions

參考文獻

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[4] C. NICULESCU AND L.-E PERSSON,Old and new on the Hermite-Hadadmard inequality, Real Anal-