International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 7, 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

Received 17 June 2003

Copyright © 2004 Ciprian S. Gal and Sorin G. Gal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.