## 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

requires subscription: https://doi.org/10.1007/s10474-016-0642-x

## About this paper

##### Journal

Acta Mathematica Hungarica

##### Publisher Name

Springer

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