Approximation aspects of set-valued fractal surfaces

The article deals with the construction of an $ \alpha $-fractal surface corresponding to a continuous compact set-valued function defined on a closed and bounded rectangular region of the Euclidean plane via an iterated function system. Additionally, the fractal function obtained follows a self-referential equation, exhibiting self-similarity in nature. Further, the condition is derived so that the fractal function is Hölder continuous. In the end, Bernstein-type fractal approximations of a continuous convex compact set-valued function are elaborated, and bounds for approximation error are estimated.