关于几何凸函数的积分型Jensen不等式

On Integral Jensen Inequation of Geometrical Convex Functions

考虑几何凸函数的几何凸性,研究了其Jensen型不等式的连续形式,利用定积分的定义和几何凸函数的一个充要条件,建立了几何凸函数的积分型Jensen不等式及其加权形式.

Considering the convexity of geometrical convex functions, the author studies the continuous form of their Jensen inequation, and sets up the integral Jensen inequation of geometrical convex functions and its weighting form by using the definition of definite integral and a necessary and sufficient condition of geometrical convex functions.