The aim of this work is to introduce the concept of an \((F,\gamma )_{\mathfrak {R}}\)-contraction which is a weak idea of an F-contraction in metric spaces endowed with a binary relation. Fixed point results for such new contractions are investigated, and its benefit is showing from an example. As applications, we apply theoretical results together with the Thompson metric for solving nonlinear matrix equations. Finally, we give a numerical example showing the usage of the proposed algorithm to solve nonlinear matrix equations.

中文翻译：

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具有关系理论F约束的基于弱条件的非线性矩阵方程解的新算法

这项工作的目的是介绍\（（（F，\ gamma）_ {\ mathfrak {R}} \）- contraction的概念，这是度量空间中具有二元关系的F-收缩的一个弱概念。研究了此类新收缩的定点结果，并从一个示例中显示了其好处。作为应用，我们将理论结果与汤普森度量一起用于求解非线性矩阵方程。最后，我们给出一个数值示例，说明所提出的算法用于求解非线性矩阵方程的用法。