Singular Functions with Applications to Fractal Dimensions and Generalized Takagi Functions
2012
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.
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