Posts by Octavian Agratini


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.


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


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

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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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