This article is devoted to explore the abilities of an iterative scheme for the approximation of fixed points of self-maps, called the N-algorithm, defined in a previous paper. In a first part of the article, the algorithm is modified in order to consider operators with asymptotic properties, namely nearly uniform contractions and nearly asymptotically nonexpansive mappings. Sufficient conditions on the (normed or quasi-normed) underlying space and the operator are given in order to ensure weak or strong convergence of the new algorithm to a fixed point.

中文翻译：

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用于固定点和分形函数近似的新算法


本文致力于探讨迭代方案在前一篇论文中定义的近似自映射的固定点的能力，称为 N 算法。在本文的第一部分，对算法进行了修改，以考虑具有渐近特性的算子，即几乎均匀的收缩和几乎渐近的非膨胀映射。给出了 （normed 或 quasi-normed） 底层空间和算子的充分条件，以确保新算法的弱收敛或强收敛到一个固定点。