- 學位論文
一些更細緻的Hadamard不等式
Some refinements of Hadamard Inequality
摘要
如果 f: [a,b] → ℝ 為[a,b]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[a,b]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
並列摘要
If f : [a,b] → ℝ is convex on [a,b], 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 [a,b] , 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)
參考文獻
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