本文中均假設 I = [a, b],f為I上的函數: 若f : I → ℝ為I中的凸函數,則 f((a+b)/2)≤1/(b-a)∫_a^b▒〖f(x)dx≤(f(a)+f(b))/2 〗, (1.1) 恆成立,為眾所週知的Hermite-Hadamard不等式。 若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≤(f(a)+f(b))/2〗, (1.2) 本論文研究的主要目的,是為了提供問題 (1.2)更多的答案。 Throughout, let I denote the closed interval [a, b] of real numbers. If f : I → ℝ is convex on I, then f((a+b)/2)≤1/(b-a)∫_a^b▒〖f(x)dx≤(f(a)+f(b))/2.〗 (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≤(f(a)+f(b))/2.〗 (1.2) The main purpose of this paper is to give more answers to the question (1.2).