Abstract This paper presents several Lipschitz implicit function theorems for maps between Banach spaces. The results use semi-inner products as a means for understanding the geometry of normed spaces. The arguments rely on corresponding geometric properties of operators on normed spaces, and on Ekeland's variational principle, in contrast with classic results such as the inverse function theorems of Nash and Moser and their use of Newton iteration procedures. The results are illustrated with an application to a central problem in mathematical economics, characterizing Lipschitz behavior of Pareto optimal allocations in a model of trade over an infinite horizon.

中文翻译：

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Banach空间中的Lipschitz隐函数定理及其应用

摘要 本文提出了Banach空间之间映射的几个Lipschitz隐函数定理。结果使用半内积作为理解赋范空间几何的手段。与经典结果（例如 Nash 和 Moser 的反函数定理及其对牛顿迭代程序的使用）相比，这些参数依赖于赋范空间上运算符的相应几何特性，以及 Ekeland 的变分原理。结果通过对数理经济学中的一个核心问题的应用来说明，在无限范围内的贸易模型中表征帕累托最优分配的 Lipschitz 行为。