Non-Differentiable Functions Defined in Terms of Classical Representations of Real Numbers
DOI:
https://doi.org/10.15407/mag14.02.197Анотація
Цю роботу присвячено деякому пiдкласу недиференцiйовних функцiй. Аргументи i значення функцiй, що розглядаються, подано через s-ве або нега-s-ве зображення дiйсних чисел. Технiка моделювання таких функцiй є простiшою в порiвняннi з добре вiдомими технiками моделювання недиференцiйовних функцiй. Iншими словами, значення цих функцiй отримано з s-го або нега-s-го зображення аргументу за допомоги певної замiни цифр чи комбiнацiй цифр.
Описано iнтегральнi, фрактальнi та iншi властивостi розглянутих функцiй.
Mathematical Subject Classification: 26A27, 11B34, 11K55, 39B22.
Ключові слова:
нiде недиференцiйовнi функцiї, s-адичнi представлення, нега-s-адичнi представлення, немонотоннi функцiї, розмiрнiсть Гаусдорфа-Безiковича.Посилання
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