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).

Table of Contents

1.Introduction........................................1
2.Main Results........................................4
References ..........................................20

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