# On a class of linear approximating operators

## Abstract

In this paper we introduce a new class of linear approximating operators $$\left( L_{nr}\right) _{n\geq1},r=0,1,2,…,$$ for the functions $$f\in C^{r}\left[ 0,1\right]$$. In order to construct them we use Taylor’s polynom of $$r$$ degree and a classical class of linear positive operators generated by a probabilistic method. Also, we study approximation degree with the modulus of continuity of first and second order. $$\left( L_{nr}\right) _{n\geq1}$$ include as a particular case the generalized Bernstein polynomials defined by G.H. Kirov in [5].

## Authors

Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

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## Paper coordinates

O. Agratini, On a class of linear approximating operators, Mathematica Balkanica N.S., 11 (1997) nos. 3-4, 407-412.

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##### Journal

Mathematica Balkanica

0205-3217