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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Differentiability through change of variables
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by A. M. Bruckner and C. Goffman PDF
Proc. Amer. Math. Soc. 61 (1976), 235-241 Request permission

Abstract:

A real function $f$ on $[0,\;1]$ can be transformed by a homeomorphism into a differentiable function with bounded derivative if and only if $f$ is continuous and of bounded variation. This condition does not suffice for $f$ to be transformed into a continuously differentiable function. The additional condition for this to hold is found and the theorem is proved.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 61 (1976), 235-241
  • MSC: Primary 26A24
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0432831-2
  • MathSciNet review: 0432831