Geometric series of positive linear operators and inverse Voronovskaya theorem

2013/04/21 by Ulrich Abel, Abel, Ulrich, Mircea Ivan +3
Mathematics · #41A27 #41A35 #41A36 #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #math.CA #msc:41A27 #msc:41A35 #msc:41A36

paper · pdf · doi:10.48550/arxiv.1304.5721

19 pages

arxiv created 2013/04/21 · openalex publication_date 2013/04/21 · openalex created_date 2016/06/24 · arxiv updated 2016/08/11 · openalex updated_date 2026/07/28

Abstract

We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our results to the Bernstein operators, the Bernstein-Durrmeyer-type operators, and the symmetrical version of Meyer-König and Zeller operators.

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