SHAPE PRESERVING ASPECTS of BIVARIATE α -FRACTAL FUNCTION

In this paper, we study shape preserving aspects of bivariate α-fractal functions. Its specific aims are: (i) to solve the range restricted problem for bivariate fractal approximation (ii) to establish the fractal analogue of lionized Weierstrass theorem of bivariate functions (iii) to study the constrained approximation by r-bivariate α-fractal functions (v) to investigate the conditions on the parameters of the iterated function system in order that the bivariate α-fractal function fα preserves fundamental shapes, namely, positivity and convexity (concavity) in addition to the smoothness of f over a rectangle (vi) to establish fractal versions of some elementary theorems in the shape preserving approximation of bivariate functions.