ON THE CLASSICAL INTEGRAL OF FRACTAL FUNCTIONS

Abstract

In this paper, the integral of classical fractal interpolation function (FIF) and A-fractal function is explored for both the cases of constant and variable scaling factors. The definite integral for the classical FIF in the closed interval of [Formula: see text] is estimated. The novel notion of affine-quadratic FIF is introduced and integrated for both constant and variable scaling factors. It is demonstrated that its integral is not an affine-quadratic FIF, however it is a FIF. Similarly, by choosing the vertical scaling factors as constants and variables, A-fractal function is integrated. Further, by assuming certain condition on the block matrix, it is shown that like the original A-fractal function its integral is also an attractor for the iterated function system.