Let be a nonempty subset of a Banach space . A mapping is said to satisfy (RCSC) condition if each , . In this paper, we study, under some appropriate conditions, weak and strong convergence for this class of maps through iterates in uniformly convex Banach space. We also present a new example of mappings with condition (RCSC). We connect iteration and other well-known processes with this example to show the numerical efficiency of our results. The presented results improve and extend the corresponding results of the literature.

中文翻译：

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Banach空间中算子满足的满意不动点（RCSC）条件

我们是Banach空间的非空子集。映射 如果每个都满足（RCSC）条件 ， 。在本文中，我们在适当的条件下，通过在均匀凸Banach空间中进行迭代来研究此类地图的弱收敛和强收敛。我们还提供了一个新的条件映射（RCSC）示例。我们将迭代和其他众所周知的过程与该示例连接起来，以显示结果的数值效率。提出的结果改进并扩展了文献的相应结果。