In this article, we enquire for a couple of weak and strong convergence results involving generalized \(\alpha \)-Reich-Suzuki non-expansive mappings in the setting of a hyperbolic metric space. Particularly, we make use of the recently proposed JF-iteration scheme to attain our theories and further, we attest that this algorithm has a faster convergence rate than that of \(M^*\) iteration. Additionally, we explore several interesting properties related to the fixed point set of such mappings and approximate fixed point sequences also. Eventually, we furnish pertinent examples to substantiate our attained findings and compare the newly proposed scheme with that of some other well-known algorithms using MATLAB 2017a software.

在本文中，我们在双曲度量空间的设置中询问涉及广义\(\alpha \) -Reich-Suzuki 非扩张映射的几个弱收敛结果和强收敛结果。特别是，我们利用最近提出的 JF 迭代方案来实现我们的理论，并进一步证明该算法具有比\(M^*\)迭代更快的收敛速度。此外，我们还探索了与此类映射的不动点集和近似不动点序列相关的几个有趣的特性。最后，我们提供了相关的例子来证实我们获得的发现，并使用 MATLAB 2017a 软件将新提出的方案与其他一些知名算法的方案进行比较。