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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
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
Published electronically: 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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Additional Information

Alexander J. Izzo
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Email: aizzo@math.bgsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04801-7
PII: S 0002-9939(99)04801-7
Received by editor(s): October 6, 1997
Published electronically: February 26, 1999
Communicated by: Hal L. Smith
Article copyright: © Copyright 1999 American Mathematical Society