The purpose of this paper is to introduce a new four-step iteration scheme for approximation of fixed point of the nonexpansive mappings named as -iteration scheme which is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our proposed scheme. We present a numerical example to show that our iteration scheme is faster than the aforementioned schemes. Moreover, we present some weak and strong convergence theorems for Suzuki’s generalized nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve, and unify many existing results in the literature.

中文翻译：

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铃木广义非扩张映象数值不动点估计的新快速迭代方案

本文的目的是介绍一种新的四步迭代方案，用于近似非膨胀映射的不动点，称为-迭代方案，它比Picard，Mann，Ishikawa，Noor，Agarwal，Abbas，Thakur和Ullah迭代快计划。我们展示了我们提出的方案的稳定性。我们提供了一个数值示例，表明我们的迭代方案比上述方案更快。此外，我们在一致凸Banach空间的框架中给出了Suzuki的广义非扩张映射的一些弱和强收敛定理。我们的结果扩展，改进和统一了文献中的许多现有结果。