The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.

中文翻译：

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两类新算子得到的某些迭代过程的等价性

本文的目的有两个：第一个是定义两个新的映射类并展示它们不动点的存在性和迭​​代逼近性；第二个是表明为此类映射定义的 Ishikawa、Mann 和 Krasnoselskij 迭代方法是等效的。还给出了主要结果在解决分裂可行性和变分不等式问题中的应用。