Estimation of Approximation with Jacobi Weights by Multivariate Baskakov Operator

Approximation Order for Multivariate Durrmeyer Operators with Jacobi Weights

and Applied Analysis 3 Since 1967, Durrmeyer introduced Bernstein-Durrmeyer operators, and there are many paperswhich studied theirproperties 1–7 . In 1991, Zhang studied the characterization of convergence forMn,1 f ;x with Jacobi weights. In 1992, Zhou 5 considered multivariate Bernstein-Durrmeyer operators Mn,d f ;x and obtained a characterization of convergence. In 2002, Xuan et al. studied...

Constrained Approximation with Jacobi Weights

In this paper, we prove that for l = 1 or 2 the rate of best l-monotone polynomial approximation in the Lp norm (1 ≤ p ≤ ∞) weighted by the Jacobi weight wα ,β(x) ∶= (1 + x)α(1 − x)β with α, β > −1/p if p <∞, or α, β ≥ 0 if p =∞, is bounded by an appropriate (l + 1)-st modulus of smoothness with the same weight, and that this rate cannot be bounded by the (l+2)-ndmodulus. Related results on con...

Multivariate Jacobi polynomials with singular weights

First we give a compact treatment of the Jacobi polynomials on a simplex in IR which exploits and emphasizes the symmetries that exist. This includes the various ways that they can be defined: via orthogonality conditions, as a hypergeometric series, as eigenfunctions of an elliptic pde, as eigenfunctions of a positive linear operator, and through conditions on the Bernstein–Bézier form. We the...

Derivatives of Multivariate Bernstein Operators and Smoothness with Jacobi Weights

Approximation by Baskakov quasi-interpolants

Baskakov operators and their inverses can be expressed as linear differential operators on polynomials. Recurrence relations are given for the computation of these coefficients. They allow the construction of the associated Baskakov quasi-interpolants (abbr. QIs). Then asymptotic results are provided for the determination of the convergence orders of these new quasi-interpolants. Finally some r...