一些更進階的Hermite-Hadamard不等式

Some More Advanced Hadamard inequality

林宏譯(Hung-Yi Lin)

指導教授 ： 陳功宇

淡江大學/理學院/數學學系碩士在職專班/碩士(2021年)

https://doi.org/10.6846/TKU.2021.00494

摘要

若函數f在[a,b]上是凸函數，則
f((a+b)/2)≦ (integral_a^b f(x) dx)/(b-a) ≦ [f(a)+f(b)]/2 恆成立
稱為Hermite-Hadamard不等式相當的有名。
A. EL FARISSI提出了一個問題:若f是一個定義在[a,b]的凸函數，
則是否存在有兩個時數l和L使得下列不等式成立:
f((a+b)/2) ≦ l(α) ≦ (integral_a^b f(x) dx)/(b-a) ≦L(α) ≦ [f(a)+f(b)]/2
本論文主要研究目的是提供上述問題的答案，並針對不一樣的l和L進行觀察

關鍵字

Hermite-Hadamard不等式

並列摘要

If f is convex function on [a,b],then
f((a+b)/2)≦ (integral_a^b f(x) dx)/(b-a) ≦ [f(a)+f(b)]/2
is known in the literature called Hermite-Hadamard inequality.There is the question that if f is convex function on [a,b],does it exist real l and L such that f((a+b)/2) ≦ l(α) ≦ (integral_a^b f(x) dx)/(b-a) ≦L(α) ≦ [f(a)+f(b)]/2
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

參考文獻

[1] D.S. Mitrinović and I.B. Lacković, Hermite and convexity, Aequat. Math., 28(1985), 229-232.

[2] S. S. D RAGOMIR AND C. E. M. PEARCE,Selected Topics on Hermite-Hadamard Inequalities,(RGMIA Monographs http://rgmia.vu.edu.au /monographs/hermite hadamard.html),Victoria University, 2000

[3] A.El.Farissi,Simple proof and refinement of Hermite-Hadamard inequality,Math ineg.ul4,No.3,(2010)365-369