Generalized Kantorovich modifications of positive linear operators

Ana-Maria Acu; Ioan Cristian Buscu; Ioan Rasa

doi:10.3934/mfc.2021042

Article Contents

2023, Volume 6, Issue 1: 54-62. Doi: 10.3934/mfc.2021042

This issue Previous Article Iterative Bernstein splines technique applied to fractional order differential equations Next Article On complex modified Bernstein-Stancu operators

Generalized Kantorovich modifications of positive linear operators

1.
Lucian Blaga University of Sibiu, Department of Mathematics and Informatics, Str. Dr. I. Ratiu, No.5-7, RO-550012 Sibiu, Romania
2.
Technical University of Cluj-Napoca, Faculty of Automation and Computer Science, Department of Mathematics, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania

^*Corresponding author: Ana-Maria Acu
^*Corresponding author: Ana-Maria Acu

Received: June 2021

Early access: January 13, 2022

Published online: January 13, 2022

This work was supported by a Hasso Plattner Excellence Research Grant (LBUS-HPI-ERG-2020-07), financed by the Knowledge Transfer Center of the Lucian Blaga University of Sibiu.

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Abstract

Starting with a positive linear operator we apply the Kantorovich modification and a related modification. The resulting operators are investigated. We are interested in the eigenstructure, Voronovskaya formula, the induced generalized convexity, invariant measures and iterates. Some known results from the literature are extended.

Keywords:

Mathematics Subject Classification: Primary: 41A36.Secondary: 41A25.

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References

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