有關一些更細緻的 Hadamard 不等式

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Title:	有關一些更細緻的 Hadamard 不等式
Other Titles:	Some refinements of Hadamard inequality
Authors:	黃維洲;Huang, Wei-Chou
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
Keywords:	Hadamard 不等式;凸函數;Hermite-Hadamard inequality;convex functions
Date:	2015
Issue Date:	2016-01-22 14:52:35 (UTC+8)
Abstract:	如果 f : I → ℝ 為I中的凸函數，則 f( (a+b)/2)≤1/(b-a ) ∫_a^b▒〖f(x)dx ≤ 1/(2 ) [f(a)+f(b)] 〗 (1.1) 恆成立，為眾所週知的Hermite-Hadamard不等式如果 f為I中的凸函數，是否存在實數 l及L 滿足下列不等式： 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) 更多的一些答案 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 some answers to the question (1.2)
Appears in Collections:	[Graduate Institute & Department of Mathematics] Thesis

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