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    Title: 關於Hadamard不等式一些更細緻的結果
    Other Titles: Several refinements of Hadamard inequality
    Authors: 古皓彰;Ku, Hao-Chang
    Contributors: 淡江大學中等學校教師在職進修數學教學碩士學位班
    楊國勝;Yang, Guo-Sheng
    Keywords: Hadamard 不等式;凸函數;Hermite-Hadamard’s inequality;Convex function
    Date: 2015
    Issue Date: 2016-01-22 14:52:23 (UTC+8)
    Abstract: 設f:Ⅰ→R是一個定義在區間Ⅰ上的凸函數,a,b∈Ⅰ a<b
    f(∑_(i=1)^n▒〖λ_i∙x_i 〗)≤∑_(i=1)^n▒〖λ_i∙f(x_i)〗對於所有 x_1,x_2,…x_n∈I 且 λ_1,λ_2,…λ_n∈[0,1]在 ∑_(i=1)^n▒λ_i =1則以下不等式成立
    f((a+b)/2)≤1/(b-a) ∫_a^b▒〖f(x)dx≤1/2 [f(a)+f(b)] (1.1)〗
    (1.1)為著名的Hadamard雙邊不等式。
    若f:Ⅰ→R是一個定義在區間Ⅰ上的凸函數,a,b∈Ⅰ a<b,是否存在兩個實數l,L滿足在以下的不等式
    f((a+b)/2)≤l≤1/(b-a) ∫_a^b▒f(x)dx≤L≤1/2 [f(a)+f(b)] (1.2)
    本論文研究的主要目的是為了提供這問題 (1.2) 更多的答案
    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)
    Appears in Collections:[數學學系暨研究所] 學位論文

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