After the establishment of the Banach contraction principle, the notion of metric space has been expanded to more concise and applicable versions. One of them is the conception of -metric, presented by Jleli and Samet. Following the work of Jleli and Samet, in this article, we establish common fixed points results of Reich-type contraction in the setting of -metric spaces. Also, it is proved that a unique common fixed point can be obtained if the contractive condition is restricted only to a subset closed ball of the whole -metric space. Furthermore, some important corollaries are extracted from the main results that describe fixed point results for a single mapping. The corollaries also discuss the iteration of fixed point for Kannan-type contraction in the closed ball as well as in the whole -metric space. To show the usability of our results, we present two examples in the paper. At last, we render application of our results.

中文翻译：

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函数加权度量空间中的一些不动点结果

在建立Banach压缩原理之后，度量空间的概念已扩展到更简洁和适用的版本。其中之一是Jleli和Samet提出的-度量的概念。在Jleli和Samet的工作之后，在本文中，我们建立了-度量空间设置中Reich型收缩的公共不动点结果。此外，还证明了，如果仅将收缩条件限制为整体的一个子集闭合球，则可以获得唯一的公共不动点-公制空间。此外，从主要结果中提取了一些重要的推论，这些结果描述了单个映射的定点结果。该推论还讨论了固定点卡纳安型收缩的迭代中闭球，以及在整个-度量空间。为了显示我们的结果的可用性，我们在本文中提供两个示例。最后，我们对结果进行了应用。