We introduce a new concept of convergence for iterative methods, named restricted global convergence, that consists of locating a solution and obtaining a domain of global convergence. As a consequence, results of semilocal convergence and local convergence are obtained. For this, we use auxiliary points and obtain balls of convergence. The study is illustrated with Chebyshev’s method.

中文翻译：

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迭代方法收敛的新概念：受限全局收敛

我们为迭代方法引入了一种新的收敛概念，称为受限全局收敛，该概念包括查找解决方案并获取全局收敛域。结果，获得了半局部收敛和局部收敛的结果。为此，我们使用辅助点并获得收敛球。这项研究用切比雪夫的方法进行了说明。