In this research, we prove strong and weak convergence results for a class of mappings which is much more general than that of Suzuki nonexpansive mappings on Banach space through the Picard–Krasnoselskii hybrid iteration process. Using a numerical example, we prove that the Picard–Krasnoselskii hybrid iteration process converges faster than both of the Picard and Krasnoselskii iteration processes. Our results are the extension and improvement of many well-known results of the literature.

中文翻译：

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Banach空间中的Picard–Krasnoselskii混合迭代过程

在这项研究中，我们证明了通过Picard-Krasnoselskii混合迭代过程，一类映射的强和弱收敛结果比Banach空间上的Suzuki非扩展映射更普遍。通过一个数值示例，我们证明了Picard-Krasnoselskii混合迭代过程的收敛速度比Picard和Krasnoselskii迭代过程都快。我们的结果是许多著名文献的扩展和改进。