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On infinite products of positive linear operators reproducing linear functions. (English) Zbl 1271.41006

Summary: Infinite products of positive linear operators reproducing linear functions are considered from a quantitative point of view. Refining and generalizing convergence theorems of Gwóźdź-Łukawska, Jachymski, Gavrea, Ivan and the present authors, it is shown that infinite products of certain positive linear operators, all taken from a finite set of mappings reproducing linear functions, weakly converge to the first Bernstein operator. A discussion of products of Meyer-König and Zeller operators is included.

MSC:

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