## Annals of Functional Analysis

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

### 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**

Received: 8 January 2019

Accepted: 10 March 2019

First available in Project Euclid: 30 October 2019

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1215/20088752-2019-0015

**Mathematical Reviews number (MathSciNet)**

MR4026370

**Zentralblatt MATH identifier**

07126074

**Subjects**

Primary: 41A10: Approximation by polynomials {For approximation by trigonometric polynomials, see 42A10}

Secondary: 41A25: Rate of convergence, degree of approximation 41A36: Approximation by positive operators 41A63: Multidimensional problems (should also be assigned at least one other classification number in this section)

**Keywords**

approximation by polynomials Bernstein polynomials Voronovskaya-type theorem

#### 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