A best constant for bivariate Bernstein and Szasz-Mirakyan operators

JOURNAL OF APPROXIMATION THEORY

卷:123

Article

De La Cal, J ; Cárcamo, J ; Valle, AM

关键词: best constants;    modulus of continuity;    Bernstein operators;    Szasz-Mirakyan operators;    bivariate operators;    binomial distribution;    Poisson distribution;   

DOI  :  10.1016/S0021-9045(03)00086-8

来源: Elsevier

【 摘 要 】

For classical Bernstein operators over the unit square, we obtain the best uniform constant in preservation of the usual l(infinity)-modulus of continuity, at the same time we show that it coincides with the corresponding best uniform constant for bivariate Szasz operators. The result validates a conjecture stated in a previous paper. The proof involves both probabilistic and analytic arguments, as well as numerical computation of some specific values. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

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