In this paper, inspired by Jleli and Samet (Journal of Inequalities and Applications 38 (2014) 1–8), we introduce two new classes of auxiliary functions and utilize the same to define ( θ , ψ ) R -weak contractions. Utilizing ( θ , ψ ) R -weak contractions, we prove some fixed point theorems in the setting of relational metric spaces. We employ some examples to substantiate the utility of our newly proven results. Finally, we apply one of our newly proven results to ensure the existence and uniqueness of the solution of a Volterra-type integral equation.

中文翻译：

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通过（θ，ψ）R-弱收缩与应用程序的新定点结果

在这篇论文中，受 Jleli 和 Samet（Journal of Inequalities and Applications 38 (2014) 1-8）的启发，我们引入了两类新的辅助函数，并利用它们来定义 ( θ , ψ ) R 弱收缩。利用 ( θ , ψ ) R - 弱收缩，我们证明了关系度量空间设置中的一些不动点定理。我们采用了一些例子来证实我们新近证明的结果的效用。最后，我们应用我们新证明的结果之一来确保 Volterra 型积分方程解的存在性和唯一性。