A recently introduced nonexpansive-type condition is subjected to an in-depth analysis. New examples are provided to highlight the relationship with Suzuki-type mappings. Furthermore, a convergence survey is conducted based on the iteration procedure Sn. Issues related to data dependence and the stability of this iterative process are also being studied. Our study is performed in the framework of Banach spaces, in which the symmetry of the associated metric is a fundamental axiom and plays a key role while proving many results of this paper.

中文翻译：

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具有条件 (D) 的运算符的迭代 Sn

对最近引入的非膨胀型条件进行了深入分析。提供了新示例以突出与 Suzuki 类型映射的关系。此外，基于迭代过程Sn进行收敛调查。与数据依赖性和此迭代过程的稳定性相关的问题也正在研究中。我们的研究是在 Banach 空间的框架中进行的，其中相关度量的对称性是一个基本公理，在证明本文的许多结果时起着关键作用。