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A best constant for bivariate Bernstein and Szász-Mirakyan operators

✍ Scribed by Jesús De La Cal; Javier Cárcamo; Ana M. Valle

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 137 KB
Volume: 123
Category: Article
ISSN: 0021-9045
DOI: 10.1016/s0021-9045(03)00086-8

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✦ Synopsis

For classical Bernstein operators over the unit square, we obtain the best uniform constant in preservation of the usual l N -modulus of continuity, at the same time we show that it coincides with the corresponding best uniform constant for bivariate Sza´sz 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.

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