Approximation Properties of λ-Bernstein-Kantorovich-Stancu Operators-Reference-Cited by-同舟云学术

Approximation Properties of λ-Bernstein-Kantorovich-Stancu Operators

Published:2022-02-01 Issue:1 Volume:72 Page:141-152
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Bodur Murat¹,Manav Nesibe²,Tasdelen Fatma¹

Affiliation:

1. Ankara University , Faculty of Science, Department of Mathematics , Tandogan , Ankara TURKEY

2. Istanbul Gelisim University , Faculty of Economy, Administrative and Social Sciences, Management Information Systems , Istanbul , TURKEY

Abstract

Abstract The goal of this paper is to construct a new type of Bernstein operators depending on the shape parameter λ ∈ [–1,1]. For these new type operators a uniform convergence result is presented. Furthermore, order of approximation in the sense of local approximation is investigated and Voronovskaja type theorem is proved. Lastly, some graphical results are given to show the rate of convergence of constructed operators to a given function f.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2022-0010/pdf

Reference18 articles.

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2. [2] BARBOSU, D.: Kantorovich-Stancu type operators, J. Inequal. Pure Appl. Math. 5(3) (2004), 1–6.

3. [3] BARBOSU, D.: The Kantorovich form of Schurer Stancu operators, Demonstr. Math. 37(2) (2004), 383–391.

4. [4] BARBOSU, D.: A survey regarding the approximation properties of the Schurer Stancu operators, Carpathian J. Math. 20(1) (2004), 1–5.

5. [5] BERNSTEIN, S. N.: Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités, Communications de la Société Mathematique de Kharkov 13(1–2) (1913).

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