## Abstract

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.

## Authors

**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

## Keywords

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.

## About this paper

##### Print ISSN

1584 – 2851

##### Online ISSN

1843 – 4401

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