The aim of this work is to usher in tripled b-metric spaces, triple weakly $\alpha _{s}$ -admissible, triangular partially triple weakly $\alpha _{s}$ -admissible and their properties for the first time. Also, we prove some theorems about coincidence and common fixed point for six self-mappings. On the other hand, we present a new model, talk over an application of our results to establish the existence of common solution of the system of Volterra-type integral equations in a triple b-metric space. Also, we give some example to illustrate our theorems in the section of main results. Finally, we show an application of primary results.

中文翻译：

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提取\（（{T}，{\ alpha __ {{s}}，{F}）\）的公共不动点定理的新结果-应用积分对三重b-度量空间中六个映射的压缩方程式

这项工作的目的是首次引入三倍的b-度量空间，三倍弱的$ \ alpha _ {s} $-可允许，三角形部分三重的弱$ \ alpha _ {s} $-可允许及其属性。此外，我们证明了关于六个自映射的重合点和公共不动点的一些定理。另一方面，我们提出了一个新模型，讨论了我们的结果的应用，以建立三重b-度量空间中Volterra型积分方程组的公共解的存在性。另外，我们在主要结果部分给出一些示例来说明我们的定理。最后，我们展示了主要结果的应用。