Power series of the operators U_n^\varrho

2014/02/13 by Heiner Gonska, Gonska, Heiner, Ioan Raşa +3
Computer Science · Mathematics · #41A10 #41A17 #41A25 #41A36 #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #math.CA #msc:41A10 #msc:41A17 #msc:41A25 #msc:41A36

paper · pdf · doi:10.48550/arxiv.1402.3216

arxiv created 2014/02/13 · openalex publication_date 2014/02/13 · arxiv updated 2014/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study power series of members of a class of positive linear operators reproducing linear function and constituting a link between genuine Bernstein-Durrmeyer and classical Bernstein operators. Using the eigenstructure of the operators we give a non-quantitative convergence result towards the inverse Voronovskaya operators. We include a quantitative statement via a smoothing approach.

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