In this paper, we establish some point of φ-coincidence and common φ-fixed point results for two self-mappings defined on a metric space via extended CG-simulation functions. By giving an example we show that the obtained results are a proper extension of several well-known results in the existing literature. As applications of our results, we deduce some results in partial metric spaces besides proving an existence and uniqueness result on the solution of system of integral equations.

中文翻译：

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属于某个给定函数的零点的公共不动点及其应用研究

在本文中，我们通过扩展的 CG 模拟函数为度量空间上定义的两个自映射建立了一些 φ 重合点和公共 φ 不动点结果。通过举一个例子，我们表明所获得的结果是现有文献中几个众所周知的结果的适当扩展。作为我们结果的应用，除了证明积分方程组解的存在性和唯一性结果外，我们还推导出了部分度量空间中的一些结果。