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Sur un Probléme de P. Scherk, Concernant la Somme des Carrés de Deux Dérivées

Published online by Cambridge University Press:  20 November 2018

Marius Iosifescu  and
Solomon Marcus
Marius Iosifescu
Affiliation:
Institut de Mathématique Bucarest, rue Eminescu, 47
Solomon Marcus
Affiliation:
Institut de Mathématique Bucarest, rue Eminescu, 47
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P. Scherk a posé le problème suivant (Canadian Mathematical Bulletin, vol.4, no. 3, 1961, p. 306, problème 49):

Let x(t) and y(t) be two differentiable functions defined in some interval. Does the function have the Darboux property?

La réponse est négative. En effet, Witold Wilkosz (Some properties of derivative functions, Fundam. Math. vol.2, 1921, p. 145−154) a montré (p. 146−147 loc. cit.) que la fonction

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 5 , Issue 2 , May 1962 , pp. 129 - 132
Copyright
Copyright © Canadian Mathematical Society 1962