SHAPE PRESERVING ASPECTS OF BIVARIATE α-FRACTAL FUNCTION

Abstract

In this paper, we study shape preserving aspects of bivariate [Formula: see text]-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 [Formula: see text]-bivariate [Formula: see text]-fractal functions (v) to investigate the conditions on the parameters of the iterated function system in order that the bivariate [Formula: see text]-fractal function [Formula: see text] preserves fundamental shapes, namely, positivity and convexity (concavity) in addition to the smoothness of [Formula: see text] over a rectangle (vi) to establish fractal versions of some elementary theorems in the shape preserving approximation of bivariate functions.