Graphs of continuous functions and fractal dimensions

In this paper, we show that, for any beta is an element of[1,2], a given strictly positive (or strictly negative) real-valued continuous function on [0, 1] whose graph has the upper box dimension less than or equal to beta can be decomposed as a product of two real-valued continuous functions on [0, 1] whose graphs have upper box dimensions equal to beta. We also obtain a formula for the upper box dimension of every element of a ring of polynomials in a finite number of continuous functions on [0, 1] over the field R.