摘要
本文对杨镇杭的“凸函数的又一性质”〔1〕的条件进行削弱,证明了:若f(x)为闭区间〔a,b〕上的可积的上凸或下凸函数,有不等式f(a)+f(b)/2成立;若函数f(x)于闭区间〔a,b〕上连续,f_+′(x)与f_+″(x)在开区间(a,b)内存在且连续,则当f_+″(x)≤0或f_+″(x)≥0时不等式(1)或(2)成立.
In this paper, the conditions of 'Another property of Convex
Funclion' are weakened. It follows that let f(x) be ingrable function of convex
superiors or convex inferiors on [a,b] . Then
or (2) holds, let function
f(x)be continuous on [a,b] , f(x)and f+'(x) exist and are contin uous in(a,b). Then if f+″(x)≤0 or f+″(x)≥0,we have inequality ( 1 ) or ( 2 ) .
