Hermite—Hadamard不等式的改进  

Refinements of Hermite-Hadamard’s inequatity

作　　者：李泽妤[1] 徐美萍[2] 宋国华[1] 

机构地区：[1]北京建筑工程学院基础部,北京100044 [2]北京工商大学数理系,北京100037

出　　处：《黑龙江大学自然科学学报》2008年第3期297-300,共4页Journal of Natural Science of Heilongjiang University

基　　金：北京市教育委员会科技发展计划面上项目(KM200410016010);北京市委组织部优秀人才资助项目(2004D0501704);高等数学优秀团队08专项资助项目

摘　　要：利用文[3]建立的Hermite—Hadamard不等式,改进了文[5]对Lipschitz函数与文[1]插值函数的结果,将文[5]中的不等式(2,2)推广为:│(f(a)+f(b))/2-(1/(b-a))∫baf(x)dx│≤(Mt/4)(b-a)即以M4代替了文[5]的M3.同时利用关于区间中点对称的点,推广了Hermite—Hadamard不等式,得到了以更精确的结果;进一步说明推广的结果是可以实现的。The results on Lipschitz function in [ 5 ] and the interpolating function in [ 1 ] are improved by mean of Hermite - Hadamard inequality established in [ 2 ]. The inequality （2.2） in [ 5 ] is generalized to ｜f（a）＋f（b）/2-1/b-a∫a^b f（x）dx｜≤Mt/4（b-a） that is, to replace M/3 in [ 5 ] to M/4. Meanwhile, Hermite - Hadard inequality is generalized by applying those points which is symmetric about the middle point of interval. The generalization is an more accurate result than before. Furthermore, it is shown that the generalization is able to be achieved.

关 键 词：凸函数 LIPSCHITZ函数 Hermite—Hadamard不等式 

分 类 号：O174[理学—数学]