Convergence of λ -Bernstein operators via power series summability method

Naim L. Braha; Toufik Mansour; M. Mursaleen; Tuncer Acar

doi:10.1007/s12190-020-01384-x

Convergence of λ -Bernstein operators via power series summability method

Naim L. Braha, Toufik Mansour, M. Mursaleen, Tuncer Acar

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we present uniform convergence of a sequence of λ -Bernstein operators via A-statistical convergence and power summability method. A rate of convergence of the sequence of operators are also investigated by means of above mentioned summability methods. The last section is devoted to pointwise convergence (A-statistical convergence) of the sequence of operators in terms of Voronovskaya and Grü ss–Voronovskaya type theorems.

Original language	English
Pages (from-to)	125-146
Number of pages	22
Journal	Journal of Applied Mathematics and Computing
Volume	65
Issue number	1-2
DOIs	https://doi.org/10.1007/s12190-020-01384-x
State	Published - Feb 2021

Bibliographical note

Publisher Copyright:
© 2020, Korean Society for Informatics and Computational Applied Mathematics.

Keywords

A-statistical convergence
Grüss–Voronovskaya type theorem
Korovkin type theorem
Power summability method
Rate of convergence
Voronovskaya type theorem
λ-Bernstein operators

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/s12190-020-01384-x

Cite this

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title = "Convergence of λ -Bernstein operators via power series summability method",

abstract = "In this paper we present uniform convergence of a sequence of λ -Bernstein operators via A-statistical convergence and power summability method. A rate of convergence of the sequence of operators are also investigated by means of above mentioned summability methods. The last section is devoted to pointwise convergence (A-statistical convergence) of the sequence of operators in terms of Voronovskaya and Gr{\"u} ss–Voronovskaya type theorems.",

keywords = "A-statistical convergence, Gr{\"u}ss–Voronovskaya type theorem, Korovkin type theorem, Power summability method, Rate of convergence, Voronovskaya type theorem, λ-Bernstein operators",

author = "Braha, {Naim L.} and Toufik Mansour and M. Mursaleen and Tuncer Acar",

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T1 - Convergence of λ -Bernstein operators via power series summability method

AU - Braha, Naim L.

AU - Mansour, Toufik

AU - Mursaleen, M.

AU - Acar, Tuncer

PY - 2021/2

Y1 - 2021/2

N2 - In this paper we present uniform convergence of a sequence of λ -Bernstein operators via A-statistical convergence and power summability method. A rate of convergence of the sequence of operators are also investigated by means of above mentioned summability methods. The last section is devoted to pointwise convergence (A-statistical convergence) of the sequence of operators in terms of Voronovskaya and Grü ss–Voronovskaya type theorems.

AB - In this paper we present uniform convergence of a sequence of λ -Bernstein operators via A-statistical convergence and power summability method. A rate of convergence of the sequence of operators are also investigated by means of above mentioned summability methods. The last section is devoted to pointwise convergence (A-statistical convergence) of the sequence of operators in terms of Voronovskaya and Grü ss–Voronovskaya type theorems.

KW - A-statistical convergence

KW - Grüss–Voronovskaya type theorem

KW - Korovkin type theorem

KW - Power summability method

KW - Rate of convergence

KW - Voronovskaya type theorem

KW - λ-Bernstein operators

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DO - 10.1007/s12190-020-01384-x

M3 - Article

AN - SCOPUS:85086833207

SN - 1598-5865

VL - 65

SP - 125

EP - 146

JO - Journal of Applied Mathematics and Computing

JF - Journal of Applied Mathematics and Computing

IS - 1-2

ER -

Convergence of λ -Bernstein operators via power series summability method

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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