Abstract The aim of this work is to establish fixed point theorems under rational type contractions in the framework of complex-valued metric spaces. These theorems extend and generalize some prominent results in the present literature. Furthermore, as an application the existence result is given for the system of Volterra–Hammerstein non-linear integral equations.

中文翻译：

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有理类型不等式在 Voltera-Hammerstein 非线性积分方程中的应用

摘要 这项工作的目的是在复值度量空间的框架内建立有理类型收缩下的不动点定理。这些定理扩展和概括了当前文献中的一些突出结果。此外，作为应用，给出了Volterra-Hammerstein非线性积分方程组的存在性结果。