SHAPE-PRESERVING BIVARIATE POLYNOMIAL APPROXIMATION IN C([-1,1]×[-1,1])

In thit paper we construct bivariate polynomials attached to a btoariate function, that approximate with Jackson-type rate involving a btoariate Ditzian-Tatik ωξmodulus of smoothness and preserve some natural kinds of bivariate monotonicity and convexity of function.The result-extends that in univariate case-of D. Leviatan in 5-6], improves that in bivariate case of the author in 3] and in some special cases, that in bivariate case of G. Anastassiou in 1].