Singular Functions with Applications to Fractal Dimensions and Generalized Takagi Functions

  • Authors:

  • E. Amo;M. Díaz Carrillo;J. Fernández-Sánchez

  • Affiliations:

  • Universidad de Almería, Almería, Spain;Universidad of Granada, Granada, Spain;Universidad de Almería, Almería, Spain

  • Venue:
  • Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
  • Year:
  • 2012

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Abstract

We study a class of singular functions via a generalized dyadic system and Hausdorff dimensions are calculated for several sets related with these functions. Furthermore, we introduce a class of monotonic type on no-interval and almost everywhere differentiable functions that includes--as an exceptional case--the continuous nowhere differentiable Takagi function (multiplied by 2) among them.