The limiting semigroup of the Bernstein iterates: degree of convergence. (English) Zbl 1121.41004

The authors study the degree of approximation of the iterated Bernstein operators to the members \((T(t))_{t\geq 0}\), of their limiting semigroup. The main result is a full quantitative description of an earlier convergence theorem obtained is S. Karlin and Z. Ziegler [J. Approx. Theory 3, 310–339 (1970; Zbl 0199.44702)].


41A10 Approximation by polynomials
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators


Zbl 0199.44702
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