# On approximation properties of Balázs-Szabados operators their Kantorovich extension

## Abstract

In this paper we deal with a sequence of positive linear operators $$\ R_{n}^{\left[ \beta \right] }$$ approximating functions on the unbounded interval $$[0,1)$$ which were firstly used by K. Balazs and J. Szabados. We give pointwise estimates in the framework of polynomial weighted function spaces. Also we establish a Voronovskaja type theoremin the same weighted spaces for $$K_{n}^{ \left[ \beta \right] }$$ operators, representing the integral generalization in Kantorovich sense of the $$R_{n}^{\left[ \beta \right] }$$.

## Authors

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

## Keywords

weighted space; linear and positive operator; Kantorovich-type operator; Voronovskaja-type theorem.

## Paper coordinates

O. Agratini, On approximation properties of Balázs-Szabados operators their Kantorovich extension, Korean Journal of Computational & Applied Mathematics, 9 (2002), 361-372

## PDF

##### Journal

Korean Journal of Computational & Applied Mathematics

1229-9502

##### Online ISSN

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