# The Takagi function: a survey

@article{Allaart2011TheTF, title={The Takagi function: a survey}, author={Pieter C. Allaart and Kiko Kawamura}, journal={Real analysis exchange}, year={2011}, volume={37}, pages={1-54} }

More than a century has passed since Takagi [75] published his simple example of a continuous but nowhere differentiable function, yet Takagi’s function – as it is now commonly referred to despite repeated rediscovery by mathematicians in the West – continues to inspire, fascinate and puzzle researchers as never before. For this reason, and also because we have noticed that many aspects of the Takagi function continue to be rediscovered with alarming frequency, we feel the time has come for a…

## 105 Citations

### On Non-homogeneity of Takagi functions

- Mathematics
- 2016

Here we study the non-homogeneity via the Assouad dimension of graphs of Takagi functions $T_{a,b}(x):[0,1]\to\mathbb{R}$ with parameters $a,b$ such that the product $ab$ is a root of a Littlewood…

### Pointwise Hölder Exponents of the Complex Analogues of the Takagi Function in Random Complex Dynamics

- Mathematics
- 2017

### ON PROPERTIES OF FUNCTIONS IN EXPONENTIAL TAKAGI CLASS

- Mathematics
- 2016

. The structure of functions in exponential Takagi class are similar to the Takagi continuous nowhere diﬀerentiable function described in 1903. These functions have one real parameter v and are…

### No-where averagely differentiable functions: Baire category and the Takagi function

- Mathematics
- 2013

A classical and well-known result due to Banach and Mazurkiewicz says that a typical (in the sense of Baire) continuous function on the unit interval is no-where differentiable. In this paper we…

### Weak tangent and level sets of Takagi functions

- MathematicsMonatshefte für Mathematik
- 2020

In this paper, we study some properties of Takagi functions and their level sets. We show that for Takagi functions $$T_{a,b}$$ T a , b with parameters a , b such that ab is a root of a Littlewood…

### On the rate of convergence for Takagi class functions

- MathematicsJapan Journal of Industrial and Applied Mathematics
- 2019

We consider a generalized version of the Takagi function, which is one of the most famous example of nowhere differentiable continuous functions. We investigate a set of conditions to describe the…

### On the rate of convergence for Takagi class functions

- MathematicsJapan Journal of Industrial and Applied Mathematics
- 2019

We consider a generalized version of the Takagi function, which is one of the most famous example of nowhere differentiable continuous functions. We investigate a set of conditions to describe the…

### Functions consistent with real numbers, and global extrema of functions in exponential Takagi class

- Mathematics
- 2020

The functions of the Takagi exponential class are similar in construction to the continuous, nowhere differentiable Takagi function described in 1901. They have one real parameter $v\in (-1;1)$ and…

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