关于<L,t>对数性凸函数的几个不等式

Some Inequalities for <L,t>Log-Convex Functions

首先在m维空间中定义了一类新的凸函数:<L,t>对数性凸函数,它是对数性凸函数的更一般形式.得到了在一维空间,任何正值连续函数都具有<L,t>对数性凸性,并推出了<L,t>对数性凸函数的一系列的新的不等式,它们都是对数性凸函数中某些相应的著名不等式的推广。

log-convex continuous log-convex Two types of convex functions are defined in a new way as the 〈L, t〉 log-convex function and the 〈L, t〉 function of the second type, which is a general form of the log-convex function.We show that any positive functions are 〈L, t〉 log-convex functions and obtain a series of inequalities for these two types of 〈L, t〉 functions, which are generalizations of famous inequalities for general 〈L, t〉 log-convex functions.