## Abstract

In this paper we are dealing with a class of summation integral operators on unbounded interval generated by a sequence \((L_{n})_{n\geq1}\) of linear and positive operators. We study the degree of approximation in terms of the moduli of smoothness of first and second order. Also we present the relationship between the local smoothness of functions and the local approximation. By using probabilistic methods, new features of \(L_{n}f\) are pointed out such as the approximation property at discontinuity points and the monotonicity property under some additional assumptions of the function \(f\) . Also the rate of convergence of these operators for functions of bounded variation is given.

## Authors

**Octavian Agratini**

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

## Keywords

summation integral operator; rate of convergence; Lupas operator; second modulus of smoothness

## Paper coordinates

O. Agratini, *On the rate of convergence of a positive approximation process*, Nihonkai Math. J., **11** (2000) no. 1, pp. 47-56.

## About this paper

##### Journal

Nihonkai Mathematical Journal

##### Publisher Name

Niigata University, Department of Mathematics

##### DOI

##### Print ISSN

1341-9951

##### Online ISSN

google scholar link

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