In this paper, we introduce extended -gauge spaces and the extended family of generalized extended pseudo--distances. Moreover, we define the sequential completeness and construct the Caristi-type -contractions in the framework of extended -gauge spaces. Furthermore, we develop periodic and fixed point results in this new setting endowed with a graph. The obtained results of this paper not only generalize but also unify and improve the existing results in the corresponding literature.

中文翻译：

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Caristi 型收缩的周期点和不动点在扩展规空间中

在本文中，我们介绍了扩展-规空间和广义增伪的大家庭-距离。此外，我们定义顺序完整性和构建Caristi不型-收缩在延伸的框架-规空间。此外，我们在这个带有图表的新环境中开发了周期性和定点结果。本文得到的结果不仅概括了，而且统一和改进了相应文献中已有的结果。