## Abstract

The starting point of this paper is the construction of a general family \(\left( L_{n}\right) _{n\geq 1}\) of positive linear operators of discrete type. Considering \(L_{n\left( k\geq 1\right) }^{k}\) the sequence of iterates of one of such operators,\(L_{n}\) our goal is to find an expression of the upper edge of the error \(\left \Vert L_{n}^{k}f-f^{\ast }\right \Vert ,f\in\left[ 0,1\right]\),where \(f^{\ast }\), is the fixed point of \(L_{n}\).The estimate makes use of the error formula for the sequence of successive approximations in Banach’s fixed point theorem and the error of approximation of the operator \(L_{n}\).Examples of special operators are inserted. Some extensions to multidimensional approximation operators are also given.

## Authors

Octavian **Agratini**

Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania

Radu **Precup**

Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania

Faculty of Mathematics and Computer Science and Institute of Advanced Studies in Science and Technology, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania

## Keywords

Positive linear operator; Bernstein operator; Stancu operator; Cheney–Sharma operator; Banach fixed point theorem; Perov fixed point theorem

## Paper coordinates

O. Agratin, R. Precup, *Estimates related to the iterates of positive linear operators and their multidimensional analogues, *Positivity, **28 **(2024) art. no. 27,

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