In this paper, some fixed point results for relation theoretic weak \(\varphi \)-contractions on cone metric spaces which is defined over a Banach algebra and equipped with a binary relation are proved. These results extend and generalize several results of metric and cone metric spaces. Some examples are provided which demonstrate the results proved herein. An application of our main result to a system of Volterra type equations is given.

中文翻译：

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具二元关系的锥度量空间中关系理论上的弱$$ \ varphi $$φ-收缩的一些不动点结果及其在Volterra型方程组中的应用

本文证明了在Banach代数上定义并具有二元关系的锥度量空间上的理论关系弱\（\ varphi \）压缩的一些不动点结果。这些结果扩展并归纳了度量和圆锥度量空间的一些结果。提供了一些示例，这些示例演示了本文证明的结果。给出了我们的主要结果在Volterra型方程组中的应用。