By studying the judgment conditions and properties of geometry convex functions based on their geometry convex and by constructing the auxiliary convex function method ,the authors set up two necessary and sufficient conditions of geometry convex functions, and bring forth their applications.%利用几何凸函数的几何凸性，研究了几何凸函数的判定条件和特性，通过构建辅助凸函数的方法，建立了几何凸函数的两个充要条件，并给出了其应用．
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