On construit une famille de fonctions continues sur l’intervalle
We construct a family of continuous functions on the unit interval which have nowhere a unilateral derivative finite or infinite by using De Rham’s functional equations. Then we show that for any
@article{AIF_1988__38_2_43_0, author = {Hata, Masayoshi}, title = {On continuous functions with no unilateral derivatives}, journal = {Annales de l'Institut Fourier}, pages = {43--62}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {38}, number = {2}, year = {1988}, doi = {10.5802/aif.1134}, mrnumber = {89i:26006}, zbl = {0641.26010}, language = {en}, url = {https://www.numdam.org/articles/10.5802/aif.1134/} }
TY - JOUR AU - Hata, Masayoshi TI - On continuous functions with no unilateral derivatives JO - Annales de l'Institut Fourier PY - 1988 SP - 43 EP - 62 VL - 38 IS - 2 PB - Institut Fourier PP - Grenoble UR - https://www.numdam.org/articles/10.5802/aif.1134/ DO - 10.5802/aif.1134 LA - en ID - AIF_1988__38_2_43_0 ER -
Hata, Masayoshi. On continuous functions with no unilateral derivatives. Annales de l'Institut Fourier, Tome 38 (1988) no. 2, pp. 43-62. doi : 10.5802/aif.1134. https://www.numdam.org/articles/10.5802/aif.1134/
[1] Über die Baire'sche Ketegorie gewisser Funktionenmengen, Studia Math., 3 (1931), 174-179. | JFM | Zbl
,[2] Mémoire sur les nombres dérivés des fonctions continues, J. Math. Pures Appl. (Ser. 7), 1 (1915), 105-240. | JFM
,[3] On asymmetrical derivates of non-differentiable functions, Canad. J. Math., 20 (1968), 135-143. | MR | Zbl
,[4] On the structure of self-similar sets, Japan J. Appl. Math., 2 (1985), 381-414. | MR | Zbl
,[5] Über die Differenzierbarkeit stetiger Funktionen, Fund. Math., 21 (1933), 48-58. | JFM | Zbl
,[6] The Theory of Functions of a Real Variable, Toronto, 1951, pp. 172-181. | MR | Zbl
,[7] Sur les fonctions non dérivables, Studia Math., 3 (1931), 92-94. | JFM | Zbl
,[8] A continuous function with no unilateral derivatives, Trans. Amer. Math. Soc., 44 (1938), 496-507. | JFM | MR | Zbl
,[9] On continuous functions without a derivative, Fund. Math., 12 (1928), 244-253. | JFM
,[10] Sur quelques courbes définies par des équations fonctionnelles, Rend. Sem. Mat. Torino, 16 (1957), 101-113. | MR | Zbl
,[11] On the functions of Besicovitch in the space of continuous functions, Fund. Math., 19 (1932), 211-219. | JFM | Zbl
,[12] On functions without one-sided derivatives I, Proc. Benares Math. Soc., 3 (1941), 55-69. | MR | Zbl
,[13] On functions without one-sided derivatives II, Proc. Benares Math. Soc., 4 (1942), 95-108. | MR | Zbl
,[14] On the derivates of non-differentiable functions, Messenger of Math., 38 (1908), 65-69. | JFM
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