In this paper, by the notions of base functionals and augmented dual cones, the authors indicate firstly that the norms, Gerstewitz functionals and oriented distance functions have common characteristics with base functionals. After that, the equivalence of these three sublinear functions on the ordering cone is established by using the structures of augmented dual cones under the assumption that it has a bounded base. However, the authors show that two superlinear functions do not have similar relations with the norms ahead. More generally, the equivalence of three sublinear functions outside the negative cone has also been obtained in the end.

中文翻译：

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向量优化中一类三个非线性标量函数的等价性。

在本文中，通过基本功能和扩充双锥的概念，作者首先指出，范数，Gerstewitz功能和定向距离功能与基本功能具有共同的特征。此后，在有序底锥的前提下，通过使用增强型双锥锥的结构，建立了这三个亚线性函数在锥面上的等价性。但是，作者表明，两个超线性函数与前面的规范没有相似的关系。更普遍地，最后还获得了负圆锥外部的三个亚线性函数的等价关系。