In this paper, we revisit two recently published papers on the iterative approximation of fixed points by Kumam et al. (2019) [17] and Maniu (2020) [19] and reproduce convergence, stability, and data dependency results presented in these papers by removing some strong restrictions imposed on parametric control sequences. We confirm the validity and applicability of our results through various non-trivial numerical examples. We suggest a new method based on the iteration algorithm given by Thakur et al. (2014) [28] to solve the two-point second-order boundary value problems. Furthermore, based on the above mentioned iteration algorithm and S-iteration algorithm, we propose two new gradient type projection algorithms and applied them to supervised learning. In both applications, we present some numerical examples to demonstrate the superiority of the newly introduced methods in terms of convergence, accuracy, and computational time against some earlier methods.

在本文中，我们将回顾Kumam等人最近发表的两篇关于定点迭代逼近的论文。（2019）[17]和Maniu（2020）[19]，并通过消除对参数控制序列施加的一些强约束来重现这些论文中提出的收敛性，稳定性和数据依赖性结果。我们通过各种非平凡的数值示例来证实我们的结果的有效性和适用性。我们建议一种基于Thakur等人给出的迭代算法的新方法。（2014）[28]解决了两点二阶边值问题。此外，基于上述迭代算法和S-迭代算法，我们提出了两种新的梯度类型投影算法，并将其应用于监督学习。在这两个应用程序中，我们都提供了一些数值示例，以证明新引入的方法在收敛性，准确性和计算时间方面优于某些早期方法。