Differentiable functions which do not satisfy a uniform Lipschitz condition of any order

Author:
Masayoshi Hata

Journal:
Proc. Amer. Math. Soc. **111** (1991), 443-450

MSC:
Primary 26A16; Secondary 26A27

DOI:
https://doi.org/10.1090/S0002-9939-1991-1045138-8

MathSciNet review:
1045138

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Abstract: The aim of this paper is to construct two kinds of absolutely continuous functions. One is differentiable *everywhere* but does not satisfy a uniform Lipschitz condition of any order on some large class of subintervals, while the other is differentiable almost everywhere but does not satisfy a uniform Lipschitz condition of any order on *any* subintervals.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1045138-8

Keywords:
Lipschitz conditions,
discontinuous derivatives

Article copyright:
© Copyright 1991
American Mathematical Society