International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 5-8, Pages 325-333
doi:10.1155/S0161171204306137
Shape-preserving multivariate polynomial approximation in C[−1,1]m
Ciprian S. Gal1
and Sorin G. Gal2
1Department of Mathematical Sciences, The University of Memphis, Memphis 38152, TN, USA
2Department of Mathematics, University of Oradea, Oradea 3700, Romania
Abstract
We construct multivariate polynomials attached to a function f of m variables, m≥2 , which approximate f with Jackson-type rate involving a multivariate Ditzian-Totik ω2φ-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.