A best constant for bivariate Bernstein and Szász-Mirakyan operators

@article{Cal2003ABC,
  title={A best constant for bivariate Bernstein and Sz{\'a}sz-Mirakyan operators},
  author={Jes{\'u}s De La Cal and Javier C{\'a}rcamo and Ana M. Valle},
  journal={Journal of Approximation Theory},
  year={2003},
  volume={123},
  pages={117-124}
}
For classical Bernstein operators over the unit square, we obtain the best uniform constant in preservation of the usual l∞-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. 

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