## Annals of Functional Analysis

### Modified $\alpha$-Bernstein operators with better approximation properties

#### Abstract

In the present note, following a new approach recently described by Khosravian-Arab, Dehghan, and Eslahchi, we construct a new kind of $\alpha$-Bernstein operator and study a uniform convergence estimate for these operators. We also prove some direct results involving the asymptotic theorems. Finally, we illustrate the convergence of the operators to a certain function with the help of Maple software.

#### Article information

Source
Ann. Funct. Anal., Volume 10, Number 4 (2019), 570-582.

Dates
Accepted: 10 March 2019
First available in Project Euclid: 30 October 2019

https://projecteuclid.org/euclid.afa/1572422414

Digital Object Identifier
doi:10.1215/20088752-2019-0015

Mathematical Reviews number (MathSciNet)
MR4026370

Zentralblatt MATH identifier
07126074

#### Citation

Kajla, Arun; Acar, Tuncer. Modified $\alpha$ -Bernstein operators with better approximation properties. Ann. Funct. Anal. 10 (2019), no. 4, 570--582. doi:10.1215/20088752-2019-0015. https://projecteuclid.org/euclid.afa/1572422414

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