Hermite-Hadmard不等式的扩张(英文)

Several Extensions of Hermite-Hadmard Inequality

著名的Hermite-Hadamard不等式可表述为:设f:[a,b]→R凸函数,则有f(a 2+b)b-1a∫abf(t)dtf(a)+f(b)2.本文给出这个不等式中的f(a 2+b)的最佳下界和(b-a)-1∫abf(t)dt的最佳上界.作为应用,获得了一些涉及两个正数a与b的平均值的不等式.

The Hermite-Hadamard Inequality says that： Let f be a convex function on [a,b] , and then f（（a＋b）/2）≤1/（b-a）∫a^bf（t）dt ≤（f（a）＋f（b））/2. In this paper, under the advisable hyoltheses, we shall give the best lowerbound of f（ （a ＋ b）/2） and the best upper bound of （b - a）^ -1∫a^bf（t）dt. As applications ,several inequalities involving the so-called extended mean values are obtained.