A Short Note on Fractal Interpolation in the Space of Convex Lipschitz Functions

In this short note, we consider fractal interpolation in the Banach space Vθ(I) of convex Lipschitz functions defined on a compact interval I⊂R. To this end, we define an appropriate iterated function system and exhibit the associated Read–Bajraktarević operator T. We derive conditions for which T becomes a Ratkotch contraction on a closed subspace of Vθ(I), thus establishing the existence of fractal functions of class Vθ(I). An example illustrates the theoretical findings.