Constrained approximation and set-valued results for a class of fractal functions

We study constrained approximation for a class of $ \alpha $-fractal interpolation functions ($ \alpha $-FIFs, for short) without endpoint conditions. Precisely, for this $ \alpha $-FIFs without endpoint conditions, we explore monotonicity, one-sided and dimension-preserving approximations. Further, we investigate specific important properties of the associated set-valued functions. We also show the existence of fractal functions in Besov space w.r.t. the fractal measure.