Shape-preserving multivariate polynomial approximation inC[−1,1]m

Ciprian S. Gal, Sorin G. Gal
2004 International Journal of Mathematics and Mathematical Sciences  
We construct multivariate polynomials attached to a functionfofmvariables,m≥2, which approximatefwith Jackson-type rate involving a multivariate Ditzian-Totikω2φ-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.
doi:10.1155/s0161171204306137 fatcat:poo3dra4qfgwjdiy3wvt3mmame