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

Gonska, H.; Raşa, I.

Acta Math. Hung. 111, No. 1-2, 119-130 (2006).

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)].

Reviewer: Zoltán Finta (Cluj-Napoca)

MSC:

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

Keywords:

Bernstein iterates; limiting semigroup; degree of convergence

Citations:

Zbl 0199.44702