On the variation detracting property of operators of Balázs and Szabados (original) (raw)

Acta Mathematica Hungarica, 2016

Abstract

In this note we spotlight the linear and positive operators of discrete type {{{(R_n)}_{n\geqq1}}}$$(Rn)n≧1 known as Balázs–Szabados operators. We prove that this sequence enjoys the variation detracting property. The convergence in variation of {{{(R_{n}f)}_{n\geqq1}}}$$(Rnf)n≧1 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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