We give some sufficient conditions for the convergence of the sequence of successive approximations to the unique solution of first order Cauchy problem in a Banach space. Our approach is based on a generalized Nagumo condition due to A. Constantin and the properties of the Kuratowski measure of noncompactness.

中文翻译：

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Banach空间中通过康斯坦丁条件的微分方程的逐次逼近

我们为连续逼近序列的收敛到Banach空间中一阶Cauchy问题的唯一解提供了一些充分的条件。我们的方法基于A. Constantin的广义Nagumo条件和Kuratowski测度的非紧致性的性质。