On the Durrmeyer-type variant and generalizations of Lototsky–Bernstein operators

Octavian Agratini
(original), Approximation Theory, ISI/JCR, paper

Abstract

The starting points of the paper are the classic Lototsky–Bernstein operators. We present an integral Durrmeyer-type extension and investigate some approximation properties of this new class. The evaluation of the convergence speed is performed both with moduli of smoothness and with K-functionals of the Peetre-type. In a distinct section we indicate a generalization of these operators that is useful in approximating vector functions with real values defined on the hypercube. The study involves achieving a parallelism between different classes of linear and positive operators, which will highlight a symmetry between these approximation processes.

 

Authors

Ulrich Abel
Fachbereich MND, Technische Hochschule Mittelhessen, Germany

Octavian Agratini
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords

Lototsky operator; Korovkin theorem; modulus of smoothness; K-functional; Durrmeyer extension

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also freely available at the publisher: https://doi.org/10.3390/sym13101841

Cite this paper as:

U. Abel, O. Agratini, On the Durrmeyer-type variant and generalizations of Lototsky–Bernstein operators, Symmetry 2021, 13 (10),  https://doi.org/10.3390/sym13101841

About this paper

Journal

Symmetry

Publisher Name

MDPI

DOI

https://doi.org/10.3390/sym13101841

Print ISSN

Not available yet.

Online ISSN

2073-8994

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