FRACTAL DIMENSION OF PRODUCT OF CONTINUOUS FUNCTIONS WITH BOX DIMENSION

This paper investigates fractal dimension of product of continuous functions with Box dimension on [Formula: see text]. For two continuous functions with different Box dimensions, the Box dimension of their product has been proved to be the larger one. Furthermore, the Box dimension of product of two continuous functions with the same Box dimension may not exist. Definitions of regular fractal and local fractal functions have been given. Product of a regular fractal function and a local fractal function with the same Box dimension must still be the original Box dimension.