A ONE-DIMENSIONAL CONTINUOUS FUNCTION WITH UNBOUNDED VARIATION

Dong Yang

doi:10.1142/S0218348X24400073

A ONE-DIMENSIONAL CONTINUOUS FUNCTION WITH UNBOUNDED VARIATION

2024-01-10

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DOI：10.1142/S0218348X24400073

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In this paper, we consider a function with only one unbounded variation point and study the box dimension of its graph. We prove that the function is continuous and differentiable on a certain interval. Moreover, we show that the function is of unbounded variation on the domain of definition. Using our techniques, we also estimate the box dimension of the graph of the function.

Keyword:

Fractal Function

Unbounded Variation

Box Dimension

A ONE-DIMENSIONAL CONTINUOUS FUNCTION WITH UNBOUNDED VARIATION

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