Representations for the inverses of certain operators

Ana-Maria Acu; Madalina Dancs; Voichiţa Adriana Radu

doi:10.3934/cpaa.2020182

Article Contents

2020, Volume 19, Issue 8: 4097-4109. Doi: 10.3934/cpaa.2020182

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Representations for the inverses of certain 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, Str. Memorandumului nr. 28 Cluj-Napoca, Romania
3.
Babes-Bolyai University, FSEGA, Department of Statistics-Forecasts-Mathematics, Cluj-Napoca, Romania

^* Corresponding author
^* Corresponding author

Received: July 31, 2019

Revised: October 31, 2019

Published: May 2020

The first author is supported by Lucian Blaga University of Sibiu & Hasso Plattner Foundation research grants LBUS-IRG-2019-05

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Abstract

Inverses of certain positive linear operators have been investigated in several recent papers, in connection with problems like decomposition of classical operators, representation of Lagrange-type operators, asymptotic formulas of Voronovskaja type. Motivated by such researches, in this paper we give some representations for the inverses of certain positive linear operators, as Bernstein, Beta, Bernstein - Durrmeyer, genuine Bernstein - Durrmeyer and Kantorovich operators. Moreover, some Voronovskaja type formulas for the inverses of these operators are obtained. Several techniques are used in order to get such results.

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Mathematics Subject Classification: Primary: 41A35, 41A36; Secondary: 41A25.

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