更細緻的Hermite-Hadamard不等式

若f：[a, b]→R 為凸函數，a, b∈ R，則 f((a+b)/2)≤1/(b-a) ∫_a^bf(x)dx≤(f(a)+f(b))/2 (1.1) 恆成立，這就是有名的Hermite-Hadamard不等式，要探討的是，若f為[a, b]中的凸函數，是否能找到實數 l 及 L 使得下列不等式能成立： f((a+b)/2)≤ l ≤1/(b-a) ∫_a^bf(x)dx≤ L ≤(f(a)+f(b))/2 本論文研究的主要目的是要對上式提供更多答案。

關鍵字

Hermite-Hadamard不等式；凸函數

並列摘要

If f:[a, b]→R is convex on [a, b],then f((a+b)/2)≤1/(b-a) ∫_a^bf(x)dx≤(f(a)+f(b))/2 (1.1) is kmown in the literature the Hermite-Hadamard inequality. There is the question that if f is a convex function on [a, b], do there exist real number l and L such that f((a+b)/2)≤l ≤1/(b-a) ∫_a^bf(x)dx≤ L ≤(f(a)+f(b))/2 The major goal of this study is to give some answers to the question

並列關鍵字

Hermite-Hadamard inequality；Convex function

參考文獻

3.參考文獻

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[1] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities (RGMIA Monographs http://rgmia.vu.edu.au/monographs/hermits_hadamard.html),Victoria University, 2000.