Uniform Continuity of Fractal Interpolation Function

Xuezai Pan, Minggang Wang, Xudong Shang, Jixiang Yang
2020 Mathematical Problems in Engineering  
In order to research analysis properties of fractal interpolation function generated by the iterated function system defined by affine transformation, the continuity of fractal interpolation function is proved by the continuous definition of function and the uniform continuity of fractal interpolation function is proved by the definition of uniform continuity and compactness theorem of sequence of numbers or finite covering theorem in this paper. The result shows that the fractal interpolation
more » ... ctal interpolation function is uniformly continuous in a closed interval which is from the abscissa of the first interpolation point to that of the last one.
doi:10.1155/2020/7840432 fatcat:actugnxqavgjrky7myuu2xvfim