Abstract In this paper, we extend the study of an iteration process introduced by Thakur-Thakur-Postolache [J. Inequal. Appl., (2014), 147–155] from the class of nonexpansive operators to the more general class of Suzuki operators. We prove weak and strong convergence theorems regarding the iteration method for mappings satisfying the condition (C) of Suzuki in uniformly convex Banach spaces. We study the stability of this iteration process, and introduce a data dependency result for the subclass of contractive operators. An example illustrates the theoretical outcome.

中文翻译：

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基于定性研究的铃木映射的三步迭代过程

摘要 在本文中，我们扩展了对 Thakur-Thakur-Postolache 引入的迭代过程的研究 [J. 不平等。Appl., (2014), 147–155] 从非膨胀算子类到更一般的铃木算子类。我们证明了关于在一致凸 Banach 空间中满足 Suzuki 条件 (C) 的映射的迭代方法的弱收敛定理和强收敛定理。我们研究了这个迭代过程的稳定性，并为收缩算子的子类引入了一个数据依赖结果。一个例子说明了理论结果。