Real Analysis Exchange

Higher Order Uniform Smoothness and Differentiability of Real Functions

Matteo Rocca and Davide La Torre

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It is known that smoothness-type conditions have several implications on continuity and differentiability properties of real functions. When these conditions hold uniformly on an interval the implications become even stronger. The aim of this paper is to extend to higher orders the relations between uniform smoothness-type conditions and differentiability, taking into account higher order divided differences.

Article information

Real Anal. Exchange, Volume 26, Number 2 (2000), 657-668.

First available in Project Euclid: 27 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15] 26A16: Lipschitz (Hölder) classes

H\"older functions divided differences


Torre, Davide La; Rocca, Matteo. Higher Order Uniform Smoothness and Differentiability of Real Functions. Real Anal. Exchange 26 (2000), no. 2, 657--668.

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