On the variation detracting property of operators of Balázs and Szabados

Abstract

In this note we spotlight the linear and positive operators of discrete type $$(R_{n})_{n\geq1}$$ known as Balazs–Szabados operators. We prove that this sequence enjoys the variation detracting property. The convergence in variation of $$(R_{n}f)_{n\geq1}$$ to f is also proved. A generalization in Kantorovich sense is constructed and boundedness with respect to BV-norm is revealed.

Authors

Ulrich Abel
Fachbereich MND, Technische Hochschule Mittelhessen, Wilhelm-Leuschner-Straße 13, 61169 Friedberg, Germany

Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

linear positive operator; function of bounded variation; variation detracting property

Paper coordinates

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

PDF

Journal

Acta Mathematica Hungarica

Springer

Online ISSN

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