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Shape-preserving bivariate polynomial approximation inC([−1,1]×[−1,1])

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Analysis in Theory and Applications

Abstract

In this paper we construct bivariate polynomials attached to a bivariate function, that approximate with Jackson-type rate involving a bivariate Ditzian-Totik ω ρ2 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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Authors and Affiliations

  1. Department of Mathematics, University of Oradea, 3700, Oradea, Romania

    Sorin G. Gal

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  1. Sorin G. Gal
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Correspondence to Sorin G. Gal.

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Gal, S.G. Shape-preserving bivariate polynomial approximation inC([−1,1]×[−1,1]). Approx. Theory & its Appl. 18, 26–33 (2002). https://doi.org/10.1007/BF02837046

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  • DOI: https://doi.org/10.1007/BF02837046

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