## 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

## Keywords

linear positive operator; sequence of random variables; modulus of continuity; expectation.

## Paper coordinates

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

## About this paper

##### Journal

Mathematica Balkanica

##### Publisher Name

##### DOI

##### Print ISSN

##### Online ISSN

0205-3217

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