更多更極致的Hadamard不等式

More refinements of Hadamard Inequality

洪睿澤(Jui-Tse Hung)

指導教授 ： 楊國勝

淡江大學/理學院/中等學校教師在職進修數學教學碩士學位班/碩士(2016年)

https://doi.org/10.6846/TKU.2016.00391

摘要

若f在[a,b]中為一個凸函數，那麼存在有實數l,L，並使得l,L介於Hadamard不等式的不等號中間嗎?
這個論文主要研究目的就是去找出更多這樣的答案。

關鍵字

Hadamard不等式 ； 凸函數

並列摘要

If f is convex function on [a,b],do there exist real numbers l,L,such that between the classic Hermite-Hadamard inequality?
The main purpose of this paper is to give more answers to the question.

並列關鍵字

Hermite-Hadamard inequality ； convex functions

參考文獻

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[2] A. EL FARISSI, Z. LATREUCH, B. BELAÏDI, Hadamard-Type Inequalities for Twice Differentiable Functions, RGMIA, Reseaech Report Collection, 12. 1 (2009), Art. 6.

[3] A. EL FARISSI, Simple proof and refinement of Hermite-Hadamard inequality, Journal of Mathematical Inequalities, Vol. 4, No. 3 (2010), 365-369.

[5] D.S. MITRINOVIĆ AND I.B. LACKOVIĆ, Hermite and convexity, Aequationes Math, 28 (1985), 229-232.

[6] C. NICULESCU AND L.E. PERSSON, Old and new on the Hermite-Hadamard inequality, Real Analysis Exchange, (2004).