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<p>The Takagi function is a classical example of a continuous nowhere differentiable function. In this paper, we study the big Lip and little lip functions of the Takagi function. First, we characterize the set of points where the big Lip function is finite and compute its minimum value. Regarding the little lip function of the Takagi function, we show that it is equal to 4/15 for almost every point in [0,&#xa0;1], which is also its minimum value. Furthermore, we characterize the set of points where the little lip function is infinite. Consequently, we conclude that this set has Hausdorff dimension one. Finally, we determine the values of the big Lip and little lip functions at various points.</p>

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The little lip and big Lip functions of the Takagi function

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • Bruce Hanson,
  • Jesús Llorente

摘要

The Takagi function is a classical example of a continuous nowhere differentiable function. In this paper, we study the big Lip and little lip functions of the Takagi function. First, we characterize the set of points where the big Lip function is finite and compute its minimum value. Regarding the little lip function of the Takagi function, we show that it is equal to 4/15 for almost every point in [0, 1], which is also its minimum value. Furthermore, we characterize the set of points where the little lip function is infinite. Consequently, we conclude that this set has Hausdorff dimension one. Finally, we determine the values of the big Lip and little lip functions at various points.