区间上似凸函数的幂平均不等式

The Power Mean Inequality Of Similarly Convex Function On Interval

定义了区间上似凸函数的概念.利用定积分的性质把凸函数的幂平均不等式Mα(f ) <Sα+1(f (a) ,f (b) ) , α∈R推广到区间上似凸函数,并证明了Hadamard不等式的右边不等式对区间上似凸函数亦成立.

Define the concept of similarly convex function on interval. Generalize the power mean inequality of convex function M_α(f)S_ α+1(f(a), f(b))to the similarly convex function on interval by using the properties of definite integral, and prove that the right inequality of Hadamard′s inequalities hold for similarly convex function on interval.