O. Thae Gun, Kang Yong Suk, Rim Myong Gil, A Method of the Best Approximation by Fractal Function, Journal of Engineering and Applied Sciences, Volume 12,Issue 6, 2017, Pages 1496-1502, ISSN 1816-949x, jeasci.2017.1496.1502, (https://makhillpublications.co/view-article.php?doi=jeasci.2017.1496.1502) Abstract: We present a method constructing a function which is the best approximation for given data and satisfies the given self-similar condition. For this, we construct a space F of local self-similar fractal functions and show its properties. Next we present a computational scheme constructing the best fractal approximation in this space and estimate an error of the constructed fractal approximation. Our best fractal approximation is a fixed point of some fractal interpolation function. Keywords: Fractal interpolation;fractal approximation;iterated function system;fractal function space;construct