In this paper we conduct local convergence analysis of the inexact Newton methods for solving the generalized equation $ 0\in f(x)+F(x) $ under the assumption of Hölder strong metric subregularity, where $ f : X \rightarrow Y $ is a single-valued mapping while $ F : X \rightrightarrows Y $ is a set-valued mapping between arbitrary Banach spaces. Our work are proceeded as twofold: we first explore fully the property of Hölder strong metric subregularity by establishing a verifiable necessary and sufficient condition as well as discussing its stability under small perturbations, and secondly, with the help of aforementioned theoretical analysis, we conclude that every sequence generated by the inexact (quasi) Newton method and staying in a neighborhood of the solution $ \bar x $ is convergent (superlinearly) of order $ p(1+q) $ where $ p $ is the order of Hölder strong metric subregularity imposed on the mapping $ f+F $ and $ q $ is the order of Hölder calmness property for the derivative $ Df $ while $ p $ and $ q $ complement each other as long as $ p(1+q)\geq 1 $.

中文翻译：

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Hölder强度量次正则性及其在不精确牛顿法收敛分析中的应用

在本文中，我们对不精确的牛顿法进行局部收敛性分析，以求解Hölder强度量次正则性的条件下的广义方程$ 0 \ in f（x）+ F（x）$，其中$ f：X \ rightarrow Y $是单值映射，而$ F：X \ rightrightarrows Y $是任意Banach空间之间的集值映射。我们的工作有两个方面：首先，我们通过建立可验证的必要条件和充分条件，并讨论其在小扰动下的稳定性，来充分探索Hölder强度量次正规性的性质，其次，在上述理论分析的帮助下，