In this paper, we extend Caristi’s fixed point theorem in metric spaces to probabilistic metric spaces, and also, we prove some common fixed point theorems for a pair of mappings satisfying a system of Caristi-type contractions in the setting of a Menger space. Two examples are given to support the main results. Furthermore, we have functional equations as an application for the main theorem.

中文翻译：

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Menger空间上的泛函型Caristi–Kirk定理及其应用

在本文中，我们将度量空间中的Caristi不动点定理扩展到概率度量空间，并且，我们证明了在Menger空间中满足一对Caristi型压缩系统的映射的一些常见不动点定理。给出两个例子来支持主要结果。此外，我们有函数方程作为主定理的应用。