Asymptotic formulae of multivariate Bernstein approximation
Journal of Approximation Theory
On the property of monotonic convergence for multivariate Bernstein-type operators
Journal of Approximation Theory
On the asymptotic approximation with bivariate operators of Bleimann, Butzer, and Hahn
Journal of Approximation Theory
Asymptotic expansions for multivariate polynomial approximation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 vol. II: interpolation and extrapolation
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Original article: Saturation in multivariate simultaneous approximation
Mathematics and Computers in Simulation
Hi-index | 7.30 |
In this paper, we study the asymptotic expansion of the partial derivatives of a sequence of linear conservative operators. We find sufficient conditions on the sequence that guarantee that such an expansion can be derived from the asymptotic formula for the nondifferentiated sequence. Our results are valid even if the operators of the sequence present difficult conservative properties different form the classical preservation of the usual convexities. We use our theorems to obtain the complete asymptotic expansions and Voronovskaja formulae for the partial derivatives of multivariate versions of the Meyer-König and Zeller operators and the Bleimann, Butzer and Hahn operators.