The aim of this article is to investigate the local convergence analysis of the multi-step Homeier-like approach in order to approximate the solution of nonlinear equations in Banach spaces, which fulfilled the Lipschitz as well as Hölder continuity condition. The Hölder condition is more relax than Lipschitz condition. Also, the existence and uniqueness theorem has been derived and found their error bounds. Numerical examples are available to appear the importance of theoretical discussions.

中文翻译：

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Banach空间中修正Homeier-Like方法的局部收敛性

本文的目的是研究类似于Homeier的多步方法的局部收敛性分析，以便近似满足Lipschitz以及Hölder连续性条件的Banach空间中非线性方程的解。Hölder条件比Lipschitz条件更放松。同样，存在性和唯一性定理已经得到推导，并找到了它们的误差范围。数值示例可用于显示理论讨论的重要性。