Shape-preserving multivariate polynomial approximation in C[−1, 1]m. (14th February 2004) - Gal, Ciprian S.; Gal, Sorin G.
Abstract : We construct multivariate polynomials attached to a functionf ofm variables, m ≥ 2, which approximatef with Jackson-type rate involving a multivariate Ditzian-Totikω 2 φ -modulus and preserve some natural kinds of multivariate monotonicity and convexity of function. The result extends the bivariate case in Gal (2002), but does not follow straight from it and requires a careful calculation.