We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed point theorem for such mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary. Examples of mappings contracting perimeters of triangles which are not contraction mappings are constructed.

中文翻译：

---

三角形收缩周长映射的不动点定理

我们考虑度量空间中的一种新型映射，其特征是三角形周长收缩的映射。结果表明，这种映射是连续的。证明了这种映射的不动点定理，并像简单的推论一样得到了经典的巴纳赫不动点定理。构造了不是收缩映射的三角形周长收缩映射的示例。