An elementary, but very useful tool for proving inequalities for polynomials with restricted zeros is the Bernstein or Lorentz representation of polynomials. In the present paper, we give two classes of Lorentz polyno...An elementary, but very useful tool for proving inequalities for polynomials with restricted zeros is the Bernstein or Lorentz representation of polynomials. In the present paper, we give two classes of Lorentz polynomials, for which the Erd?s-type inequality holds.展开更多
In this paper, we investigate the negative extremums of fundamental functions of Lagrange interpolation based on Chebyshev nodes. Moreover, we establish some companion results to the theorem of J. Szabados on the posi...In this paper, we investigate the negative extremums of fundamental functions of Lagrange interpolation based on Chebyshev nodes. Moreover, we establish some companion results to the theorem of J. Szabados on the positive extremum.展开更多
We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, ...We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.展开更多
In this note, we establish a companion result to the theorem of J. Szabados on the maximum of fundamental functions of Lagrange interpolation based on Chebyshev nodes.
In this paper, we give error estimates for the weighted approximation of rmonotone functions on the real line with Freud weights by Bernstein-type operators.
In the present paper, we obtain estimations of convergence rate derivatives of the q-Bernstein polynomials Bn （f, qn ;x） approximating to f＇ （x） as n →∞, which is a general- ization of that relating the classic...In the present paper, we obtain estimations of convergence rate derivatives of the q-Bernstein polynomials Bn （f, qn ;x） approximating to f＇ （x） as n →∞, which is a general- ization of that relating the classical case qn = 1. On the other hand, we study the conver- gence properties of derivatives of the limit q-Bernstein operators B∞（f, q;x） as q→1-.展开更多
基金supported by the National Natural Science Foundation of China under Grant No. 11571362
文摘An elementary, but very useful tool for proving inequalities for polynomials with restricted zeros is the Bernstein or Lorentz representation of polynomials. In the present paper, we give two classes of Lorentz polynomials, for which the Erd?s-type inequality holds.
文摘In this paper, we investigate the negative extremums of fundamental functions of Lagrange interpolation based on Chebyshev nodes. Moreover, we establish some companion results to the theorem of J. Szabados on the positive extremum.
基金Supported by the National Nature Science Foundation.
文摘We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.
文摘In this note, we establish a companion result to the theorem of J. Szabados on the maximum of fundamental functions of Lagrange interpolation based on Chebyshev nodes.
基金Supported by the National Natural Science Foundation, 10601065
文摘In this paper, we give error estimates for the weighted approximation of rmonotone functions on the real line with Freud weights by Bernstein-type operators.
文摘In the present paper, we obtain estimations of convergence rate derivatives of the q-Bernstein polynomials Bn （f, qn ;x） approximating to f＇ （x） as n →∞, which is a general- ization of that relating the classical case qn = 1. On the other hand, we study the conver- gence properties of derivatives of the limit q-Bernstein operators B∞（f, q;x） as q→1-.
