關於Hadamard不等式一些更細緻的結果

Several refinements of Hadamard inequality

古皓彰(Hao-Chang Ku)

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.2015.00954

摘要

設f:Ⅰ→R是一個定義在區間Ⅰ上的凸函數，a,b∈Ⅰ a

關鍵字

Hadamard 不等式 ； 凸函數

並列摘要

If f : I → ℝ is convex on I, then
f((a+b)/2)≤1/(b-a ) ∫_a^b▒〖f(x)dx ≤ 1/(2 ) [f(a)+f(b)] 〗 (1.1)
This is the classical Hermite-Hadamard inequality
If f is a convex function on I , do there exist real numbers
l , L such that
f((a+b)/2)≤ l ≤1/(b-a ) ∫_a^b▒〖f(x)dx ≤L ≤ 1/(2 ) [f(a)+f(b)] 〗 (1.2)
The main purpose of this paper is to give more answers to
the question (1.2)

並列關鍵字

Hermite-Hadamard’s inequality ； convex function

參考文獻

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