On the dimensional connection between a class of real number sequences and local fractal functions with a single unbounded variation point

In this paper, we investigate the connection between a class of real number sequences and local fractal functions in terms of fractal dimensions. Under certain conditions, we show that the Box dimension of the graph of a local fractal function with a single unbounded variation point is equal to that of its zero points set plus one. Several concrete examples of such functions whose Box dimension can take any numbers belonging to [1 , 2] have also been given. This work may provide new approaches to the construction of various local fractal functions with the required Box dimension in the future.