關於一些更細緻的Hermite-Hadamard不等式的研究

Further Refinements of Hermite-Hadamard Inequality

王瑋萱(Wei-Hsuan Wang)

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(2015年)

https://doi.org/10.6846/TKU.2015.00897

摘要

設 f : 為凸函數(convex function)，其中a, b I, a< b，則下列不等式恆成立
此為廣為人知的Hadamard雙邊不等式。
本文試著就此Hadamard雙邊不等式，建立一些推廣與更細緻的結果。

關鍵字

Hadamard不等式 ； 凸函數

並列摘要

The following double inequality
holds for all convex functions on [a, b] is known in the literature as Hermite- Hadamard inequality.
The main purpose of this paper is to establish some generalizations and refinements of the inequality

並列關鍵字

Hadamard's double inequality ； convex functions

參考文獻

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[3]. S.S. Dragomir, Two Mappings in connection to Hadamard’s inequalities, J. Math. Anal. Appl. 167(1992)49-56.

[5]. D.S.Mistrinovie, Analytic Inequalities, Spring. Verlag, Berlin, New Yark 1970.

[6]. B.G, Pachpatte, On Some Inequalities for convex functions RGMIA Res/Cull. G(E)(2003) http://rgmia.vu.edu.au/v6(E).html.