In this paper, we first define a new pseudo-metric d on a normed linear space X. We do this by introducing two different classes of elementary topical functions. Next, we use this pseudo-metric d to investigate the non-expansivity and some properties of topical functions. Finally, the characterizations of fixed points of topical functions are given, and a relation between the pseudo-metric d and the original norm of the normed linear space X is presented.

中文翻译：

---

用新的伪度量论对局部函数的非扩张性

在本文中，我们首先在赋范线性空间X上定义了一个新的伪度量d。为此，我们引入了两种不同的基本主题功能类。接下来，我们使用该伪度量d来研究局部函数的非扩张性和某些性质。最后，给出了局部函数不动点的刻画，并给出了伪度量d与赋范线性空间X的原始范数之间的关系。