Perturbation error analysis for fractal interpolation functions and their moments

A perturbed iterated function system (IFS) is first constructed on the basis of an IFS determined in this work. The relations between the fractal interpolation function (FIF) generated with the IFS determined and the FIF generated with the corresponding perturbed IFS are investigated. The expression for the perturbation error for the two FIFs is presented by means of a derived refinement equation. In addition, the error between the moments of the two FIFs is also discussed, and a concrete error estimate is obtained.