A theorem of synthetic algorithm is proved by local quasi contraction mapping.

对局部拟压缩映射进行了讨论，并得到了关于综合算法的一个定理。

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Using the contraction mapping principle, we proved a theorem about the existence of solution for initial value problem of a class of implicit ordinary differential equations of the first order.

本文应用压缩映象原理证明了一阶隐式微分方程解的存在唯一性定理。

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