A kantorovich variant of a generalized bernstein operators

Arun Kajla; Praveen Agarwal; Serkan Araci

doi:10.22436/jmcs.019.02.03

A kantorovich variant of a generalized bernstein operators

Arun Kajla
, Praveen Agarwal
, Serkan Araci

Central University of Haryana
International College of Engineering
Hasan Kalyoncu University

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

7 Scopus citations

Abstract

In this note we present a Kantorovich variant of the operators proposed by [X. Y. Chen, J. Q. Tan, Z. Liu, J. Xie, J. Math. Anal. Appl., 450 (2017), 244-261] based on non-negative parameters. Here, we prove an approximation theorem with the help of Bohman-Korovkin’s principle and study the estimate of the rate of approximation by using the modulus of smoothness and Lipschitz type function for these operators. Also, we establish Voronovskaja type theorem and Korovkin type A-statistical approximation theorem of these operators.

Original language	English
Pages (from-to)	86-96
Number of pages	11
Journal	Journal of Mathematics and Computer Science
Volume	19
Issue number	2
DOIs	https://doi.org/10.22436/jmcs.019.02.03
State	Published - 2019
Externally published	Yes

Keywords

A-statistical convergence
Global approximation
Kantorovich operators
Modulus of continuity
Rate of convergence

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10.22436/jmcs.019.02.03

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AU - Agarwal, Praveen

AU - Araci, Serkan

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AB - In this note we present a Kantorovich variant of the operators proposed by [X. Y. Chen, J. Q. Tan, Z. Liu, J. Xie, J. Math. Anal. Appl., 450 (2017), 244-261] based on non-negative parameters. Here, we prove an approximation theorem with the help of Bohman-Korovkin’s principle and study the estimate of the rate of approximation by using the modulus of smoothness and Lipschitz type function for these operators. Also, we establish Voronovskaja type theorem and Korovkin type A-statistical approximation theorem of these operators.

KW - A-statistical convergence

KW - Global approximation

KW - Kantorovich operators

KW - Modulus of continuity

KW - Rate of convergence

UR - https://www.scopus.com/pages/publications/85072267074

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SP - 86

EP - 96

JO - Journal of Mathematics and Computer Science

JF - Journal of Mathematics and Computer Science

IS - 2

ER -

A kantorovich variant of a generalized bernstein operators

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Keywords

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