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On the variation detracting property of operators of Balázs and Szabados

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Abstract

In this note we spotlight the linear and positive operators of discrete type \({{{(R_n)}_{n\geqq1}}}\) known as Balázs–Szabados operators. We prove that this sequence enjoys the variation detracting property. The convergence in variation of \({{{(R_{n}f)}_{n\geqq1}}}\) to f is also proved. A generalization in Kantorovich sense is constructed and boundedness with respect to BV-norm is revealed.

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Authors and Affiliations

  1. Fachbereich MND, Technische Hochschule Mittelhessen, Wilhelm-Leuschner-Straße 13, 61169, Friedberg, Germany

    U. Abel

  2. Babeş–Bolyai University, Faculty of Mathematics and Computer Science, Street M. Kogălniceanu 1, 400084, Cluj-Napoca, Romania

    O. Agratini

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  1. U. Abel
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  2. O. Agratini
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Correspondence to O. Agratini.

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Abel, U., Agratini, O. On the variation detracting property of operators of Balázs and Szabados. Acta Math. Hungar. 150, 383–395 (2016). https://doi.org/10.1007/s10474-016-0642-x

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  • DOI: https://doi.org/10.1007/s10474-016-0642-x

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