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  1. No Access

    Article

    On Bernstein inequalities for multivariate trigonometric polynomials in Lp, 0 ⩽ p ⩽ ∞

    Let \({{\mathbb{T}}_n}\) be the space of all trigonometric polynomials of degree not greater than n with complex coefficients. ...

    Laiyi Zhu, **ngjun Zhao in Czechoslovak Mathematical Journal (2022)

  2. No Access

    Article

    Weighted approximation of r-monotone functions on the real line by Bernstein operators

    In this paper, we give error estimates for the weighted approximation of r-monotone functions on the real line with Freud weights by Bernstein-type operators.

    Laiyi Zhu, **aojie Zhu, **ng Liu in Analysis in Theory and Applications (2011)

  3. No Access

    Article

    Saturation theorems for generalized Bernstein polynomials

    In the present paper, we give the explicit formula of the principal part of $$ \sum\limits_{k = 0}^n {([k]_q - [n]_q x)^s x^k } \prod...

    Laiyi Zhu, Qiu Lin in Analysis in Theory and Applications (2009)

  4. No Access

    Article

    On Lagrange interpolation for |X| α (0 < α < 1)

    We study the optimal order of approximation for |x| α (0 < α < 1) by Lagrange interpolation polynomials based on Chebyshev nodes of the first kind. It is proved that the Jackson...

    Laiyi Zhu, Zhiyong Huang in Analysis in Theory and Applications (2009)

  5. No Access

    Article

    On Newman-type rational interpolation to |x| at the Chebyshev nodes of the second kind

    Recently Brutman and Passow considered Newman-type rational interpolation to |x| induced by arbitrary set of symmetric nodes in [−1, 1] and gave the general estimation of the approximation error. By their methods...

    Laiyi Zhu, Zhaolin Dong in Analysis in Theory and Applications (2006)

  6. No Access

    Article

    Approximation properties of lagrange interpolation polynomial based on the zeros of (1 −x 2 cosnarccosx

    We study some approximation properties of Lagrange interpolation polynomial based on the zeros of (1 − x2)cosnarccosx. By using a decomposition for f(x) ∈ CrCr+1 we obtain an estimate of ‖f(x)−Ln+2(f, x)‖ which r...

    Laiyi Zhu in Analysis in Theory and Applications (2006)