The Uniform Convergence Property of Sequence of Fractal Interpolation Functions in Complicated Networks

Abstract

In order to further research the relationship between fractals and complicated networks in terms of self-similarity, the uniform convergence property of the sequence of fractal interpolation functions which can generate self-similar graphics through iterated function system defined by affine transformation is studied in this paper. The result illustrates that it is can be proved that the sequence of fractal interpolation functions uniformly converges to its limit function and its limit function is continuous and integrable over a closed interval under the uniformly convergent condition of the sequence of fractal interpolation functions. The following two conclusions can be indicated. First, both the number sequence limit operation of the sequence of fractal interpolation functions and the function limit operation of its limit function are exchangeable over a closed interval. Second, the two operations of limit and integral between the sequence of fractal interpolation functions and its limit function are exchangeable over a closed interval.