Shape-preserving bivariate polynomial approximation inC([−1,1]×[−1,1]) |
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摘 要: | In this paper we construct bivariate polynomials attached to a bivariate function, that approximate with Jackson-type rate involving a bivariate Ditzian-Totik ω2-modulus 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].
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