Abstract In this paper, we introduce a new discontinuous operator and investigate the existence and uniqueness of fixed points for the operators in complete metric spaces. We also provide rate of convergence and data dependency of S-iterative scheme for a fixed point of the discontinuous operators in Banach spaces. Moreover, we prove the estimation Collage theorems and compare error estimate between data dependency and Collage theorems. Numerical examples are provided to support our results.

中文翻译：

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基于收敛分析的新迭代过程对不连续算子数据相关性的误差估计

摘要 在本文中，我们引入了一种新的不连续算子，并研究了这些算子在完全度量空间中不动点的存在性和唯一性。我们还为 Banach 空间中不连续算子的不动点提供了 S 迭代方案的收敛率和数据依赖性。此外，我们证明了估计 Collage 定理，并比较了数据依赖和 Collage 定理之间的误差估计。提供了数值示例来支持我们的结果。