MG－凸函数及其Jensen不等式

MG-CONVEX FUNCTION ＆amp; JENSEN-TYPE INEQUALITY

基于对凸性及其广义凸性的进一步考虑，提出了MG-凸函数的概念，研究了MG-凸函数的凸性特征，给出了MG-凸函数判定方法、运算性质，建立了关于MG-凸函数的离散型Jensen不等式，并指出几何凸函数、对数凸函数（AG-凸函数）、HG-凸函数都是其特殊形式。

After deeply studying the convexity and the broad convexity of convex functions,we bring forward the concept of MG-convex functions,discuss the convex properties of MG-convex functions,give the theorem and the operational properties of MG-convex functions,and set up the discrete Jensen-type inequality of MG-convex functions.We think that geometrical convex functions,AG-convex functions,and HG-convex functions are special forms of convex functions.