On approximation of unbounded functions by certain modified Bernstein operators

Radu Păltănea

doi:10.3934/mfc.2023014

Article Contents

2023, Volume 6, Issue 3: 512-519. Doi: 10.3934/mfc.2023014

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On approximation of unbounded functions by certain modified Bernstein operators

Radu Păltănea^1, ,

1.
Transilvania University of Braşov, Romania

^*Corresponding author: Radu Păltănea
^*Corresponding author: Radu Păltănea

Received: October 2022

Revised: January 2023

Early access: March 13, 2023

Published online: March 13, 2023

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Abstract

We show that by a simple modification of the Bernstein operators one can obtain a polynomial approximation of unbounded functions which admit an asymptote at an end point of the interval and we give a typical example. We define a certain modulus of continuity which allow to give a quantitative result for the degree of approximation and to make more explicit the class of functions which can be approximate. Finally we show that these operators could be transformed in order to obtain linear positive operators for approximation of functions on interval $ [0, \infty) $. The scheme used in this paper is applicable in more general cases.

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Mathematics Subject Classification: Primary: 41A36, 41A25; Secondary: 41A10.

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References

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