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 Ho<spacing diaeresis>lder 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.