Annals of Functional Analysis

Modified α-Bernstein operators with better approximation properties

Arun Kajla and Tuncer Acar

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Abstract

In the present note, following a new approach recently described by Khosravian-Arab, Dehghan, and Eslahchi, we construct a new kind of α-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


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