An Analysis of Katsuura’s Continuous Nowhere Differentiable Function
نویسنده
چکیده
منابع مشابه
The Prevalence of Continuous Nowhere Differentiable Functions
In the space of continuous functions of a real variable, the set of nowhere dilferentiable functions has long been known to be topologically "generic". In this paper it is shown further that in a measure theoretic sense (which is different from Wiener measure), "almost every" continuous function is nowhere dilferentiable. Similar results concerning other types of regularity, such as Holder cont...
متن کاملFractional differentiability of nowhere differentiable functions and dimensions.
Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the "critical order" 2-s and not so for orders between 2-s and 1, where s, 1<s<2 is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local ...
متن کاملWhen Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane?
1. Y. Baba, On maxima of Takagi–van der Waerden functions, Proc. Amer. Math. Soc. 91 (1984) 373–376. 2. P. Billingsley, Van der Waerden’s continuous nowhere differentiable function, this MONTHLY 89 (1982) 691. 3. A. M. Bruckner, J. B. Bruckner, and B. S. Thomson, Real Analysis, Prentice Hall, Upper Saddle River, NJ, 1997. 4. F. S. Cater, On van der Waerden’s nowhere differentiable function, thi...
متن کاملInclusion of Zeros of Nowhere Differentiable n-Dimensional Functions
A method is described for calculating verified error bounds for zeros of a system of nonlinear equations f(x) = 0 with continuous f : IR → IR. We do not require existence of partial derivatives of f , and the function f may even be known only up to some finite precision ε > 0. An inclusion may contain infinitely many zeros of f . An example of a continuous but nowhere differentiable function is...
متن کاملEverywhere Continuous Nowhere Differentiable Functions
Here I discuss the use of everywhere continuous nowhere differentiable functions, as well as the proof of an example of such a function. First, I will explain why the existence of such functions is not intuitive, thus providing significance to the construction and explanation of these functions. Then, I will provide a specific detailed example along with the proof for why it meets the requireme...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005