In this paper, we employ the notion asymptotic contraction of Kirk (J Math Anal Appl 277:645–650, 2003) to obtain some common fixed point results of a pair of mappings and a finite family of mappings. To execute this, we introduce the notion of asymptotic contractions in pair for a finite family of mappings. Then, we obtain our prescribed common fixed point results using these asymptotic contractions in pair concepts. After this, we apply these results to analyze the unique common solution to a certain kind of pair of matrix equations. Finally, we provide some numerical examples to authenticate our results using figurative presentations.

中文翻译：

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渐近收缩的公共不动点及其在矩阵方程中的应用

在本文中，我们采用Kirk的概念渐近收缩（J Math Anal Appl 277：645–650，2003）来获得一对映射和有限映射族的一些公共不动点结果。为了执行此操作，我们为有限映射族引入成对渐近收缩的概念。然后，使用成对概念中的这些渐近收缩来获得规定的公共不动点结果。之后，我们将这些结果用于分析某类矩阵方程对的唯一公共解。最后，我们提供一些数值示例，以使用图形表示法验证我们的结果。