Iterates of multidimensional approximation operators via Perov theorem


The starting point is an approximation process consisting of linear and positive operators. The purpose of this note is to establish the limit of the iterates of some multidimensional approximation operators. The main tool is a Perov’s result which represents a generalization of Banach fixed point theorem. In order to support the theoretical aspects, we present three applications targeting respectively the operators Bernstein, Cheney-Sharma and those of binomial type. The last class involves an incursion into umbral calculus.


Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Radu Precup
Institute of Advanced Studies in Science and Technology, Babes-Bolyai University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy


Linear positive operator, contraction principle, Perov theorem, Bernstein operator, CheneySharma operator, umbral calculus, binomial operator.

Paper coordinates

O. Agratini, R. Precup, Iterates of multidimensional approximation operators via Perov theorem, Carpathian J. Math., 38 (2022) no. 3, pp. 539-546,


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Carpathian Journal Math.

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1584 – 2851

Online ISSN

1843 – 4401

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