指数凸函数算术平均值下界的改进

The Improvement of the Lower Bound Estimate of the Arithmetic Mean for Exponential Convex Functions

利用凸函数的性质,证明了指数凸函数单侧导数的存在性,并通过不等式建立了指数凸函数与其单侧导数的联系.在此基础上,获得指数凸函数算术平均值的下界,改进了已有结果.

Using the properties of convex functions,the existence of unilateral derivatives of exponential convex functions is proved,and the relation between exponential convex functions and its derivative is established through inequalities.On this basis,the lower bounds of the arithmetic mean for exponential convex functions are obtained,which improve the existing results.