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1991•Proceedings of the American Mathematical SocietyOpen access

Differentiable Functions which do not Satisfy a Uniform Lipschitz Condition of any Order

Masayoshi Hata

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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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What this paper is about

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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Available 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.

Key concepts: Lipschitz continuity, Differentiable function, Almost everywhere, Mathematics, Order (exchange), Class (philosophy), Lipschitz domain, Construct (python library)

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