【摘要】 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。更多还原

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