𝐶^{𝑟} convergence of Picard’s successive approximations

Izzo, Alexander

doi:10.1090/S0002-9939-99-04801-7

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ISSN 1088-6826(online) ISSN 0002-9939(print)

$\boldsymbol{C}^{r}$ convergence
of Picard's successive approximations

Author: Alexander J. Izzo
Journal: Proc. Amer. Math. Soc. 127 (1999), 2059-2063
MSC (1991): Primary 34A12, 34A45
Posted: February 26, 1999
MathSciNet review: 1486736
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Abstract | References | Similar Articles | Additional Information

Abstract: A simple, elementary proof of the existence, uniqueness, and
smoothness of solutions to ordinary differential equations is given. In fact, it is shown that for a differential equation of class $C^{r}$ , the successive approximations of Picard converge in the $C^{r}$ -sense.

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