The purpose of this paper to establish the semilocal convergence analysis of three-step Kurchatov method under weaker conditions in Banach spaces. We construct the recurrence relations under the assumption that involved first-order divided difference operators satisfy the \(\omega \) condition. Theorems are given for the existence-uniqueness balls enclosing the unique solution. The application of the iterative method is shown by solving nonlinear system of equations and nonlinear Hammerstein-type integral equations. It illustrates the theoretical development of this study.

中文翻译：

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弱条件下三步Kurchatov方法的半局部收敛性

本文旨在建立弱条件下Banach空间中三步Kurchatov方法的半局部收敛性分析。我们在涉及一阶除法算符满足\（\ omega \）条件的假设下构造递归关系。给出了包围唯一解的存在唯一性球的定理。通过求解非线性方程组和非线性Hammerstein型积分方程，表明了迭代方法的应用。它说明了这项研究的理论发展。