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2001/2002 Strongly ℚ-Differentiable Functions
Zoltán Boros
Real Anal. Exchange 27(1): 17-26 (2001/2002).


A real function is called strongly $\mathbb{Q}$-dif\-fer\-en\-ti\-able if, for every real number $ h \,$, the limit of the ratio $ \left( f(x+rh) - f(x) \right) / r $ exists whenever $x$ tends to any fixed real number and $r$ tends to zero through the positive rationals. After examining the dependence of strong $\mathbb{Q}$-derivatives on their parameters, we prove that every strongly $\mathbb{Q}$-dif\-fer\-en\-ti\-able function can be represented as the sum of an additive mapping and a continuously dif\-fer\-en\-ti\-able function.


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Zoltán Boros. "Strongly ℚ-Differentiable Functions." Real Anal. Exchange 27 (1) 17 - 26, 2001/2002.


Published: 2001/2002
First available in Project Euclid: 6 June 2008

zbMATH: 1014.26011
MathSciNet: MR1887678

Primary: 26A24 , 26A30 , 39B22

Keywords: additive function , differentiability , Real function

Rights: Copyright © 2001 Michigan State University Press

Vol.27 • No. 1 • 2001/2002
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