Based on the work of Mauldin and Williams [‘On the Hausdorff dimension of some graphs’,Trans. Amer. Math. Soc.298(2) (1986), 793–803] on convex Lipschitz functions, we prove that fractal interpolation functions belong to the space of convex Lipschitz functions under certain conditions. Using this, we obtain some dimension results for fractal functions. We also give some bounds on the fractal dimension of fractal functions with the help of oscillation spaces.
No takes yet. Share an insight, caveat, or question.
Chandra et al. (2022) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: