CONSTRUCTION OF MONOTONOUS APPROXIMATION BY FRACTAL INTERPOLATION FUNCTIONS AND FRACTAL DIMENSIONS

In this paper, we research on the dimension preserving monotonous approximation by using fractal interpolation techniques. A constructive result of the approximating sequence of self-affine continuous functions has been given, which can converge to the object continuous function of bounded variation on [ 0 , 1 ] monotonously and unanimously, meanwhile their graphs can be any value of the Hausdorff and the Box dimension between one and two. Further, such approximation for continuous functions of unbounded variation or even general continuous functions with non-integer fractal dimension has also been discussed elementarily.