Fractal functions with function scaling factors as solutions of (0,4) lacunary interpolation problem

This article aims to present a family of fractal functions that provides solutions to a (0, 4) lacunary interpolation problem based on methodology of fractal perturbation with function scaling factors. Approximation orders for the proposed class of fractal interpolants and their derivatives are provided. With an eye towards “optimal” perturbation, a strategy to select suitable constant scaling factors is outlined.