- 學位論文
一些更改良的Hermite-Hadamard不等式
Several Improvements of Hermite-Hadamard Inequality
摘要
設f：[a,b]→R是一個定義在[a,b]的凸函數，則(數學公式請參照電子檔或紙本論文) (1.1)式是著名的Hermite-Hadamard雙邊不等式。 若f是一個定義在[a,b]的凸函數，則是否存在有兩個實數k,K 使得(數學公式請參照電子檔或紙本論文)(1.2) 此為參考文獻[2]中的作者提出的問題，該作者也提供了一個答案 本論文主要目的是提供更多問題(1.2)的答案。
並列摘要
If f：[a,b]→R is convex on [a,b],then (Please refer to the paper)(1.1) This is the classic Hermite-Hadamard inequality In [2],the author ask the following problem: If f is convex function on [a,b],do there exist real numbersk,K such that (Please refer to the paper)(1.2) and he gave an affirmative answer. The main purpose of this paper is to give more answers to the question.(1.2)
參考文獻
[1] S. S. Dragomir 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.
[2] A El Farissi, Simple proof and refinement of Hermite-Hadamard
延伸閱讀
- 陳宏明（2018）。關於一些改良的 Hermite-Hadamard 不等式的研究〔碩士論文，淡江大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0002-1309201815511800
- 温麗東（2016）。一些更精細的 Hermite-Hadamard 不等式〔碩士論文，淡江大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0002-2805201615251200
- 卓羿廷（2017）。一些更精細的 Hermite-Hadamard 不等式〔碩士論文，淡江大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0002-2205201720283100
- 林宏譯（2021）。一些更進階的Hermite-Hadamard不等式〔碩士論文，淡江大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0002-2001202108465000
- Yiu, H. Y. (2020). More Refinements of Hermite-Hadamard inequality [master's thesis, Tamkang University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0002-2101202016172900