若f: [a,b]→R為凸函數, a,b∈R , 則f((a+b)/2) ≤ 1/(b-a)∫_a^b f(x)dx ≤ 1/(2) [f(a)+f(b)]恆成立, 這就是著名的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?本論文研究的主要目的是要對上式提供改良答案。

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)]  is known 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 numbers l and L such that? The major goal of this study is to give improvement answers to the question.

1.緒論 1
2.主要結果 3
3.文獻探討 21

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