AI 中文总结
本文结合多项式压缩与路径平均压缩概念引入路径平均多项式压缩，证明了其在度量空间中的不动点定理，并举例说明它并非巴拿赫压缩，实现了对相关压缩概念的推广。
AI 中文摘要
多项式压缩的概念出现在[2]中，而路径平均压缩的概念分别在[3]（度量空间）、[4,5]（b - 度量空间）以及[6]（超度量空间）中出现。本文将这两个概念结合引入路径平均多项式压缩，作为多项式压缩、路径平均压缩和巴拿赫压缩的推广。在度量空间设置下得到此类压缩的不动点定理，并给出一个例子表明路径平均多项式压缩不是巴拿赫压缩。
英文摘要
The notion of polynomial contraction appeared in [2], whilst the notion of path-averaged contraction appeared in [3] for metric spaces, in [4,5] for b-metric spaces, , and in [6] for suprametric spaces. In this paper, we combine both notions to introduce path-averaged polynomial contractions, as a generaliation of polynomial contractions, path-averaged contractions, and Banach contractions.We obtain a fixed point theorem for such contractions in the setting of metric spaces.We give an example showing path-averaged polynomial contractions are not Banach contractions
