A Kantorovich variant of a generalized Bernstein operators
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Authors
Arun Kajla
- Department of Mathematics, Central University of Haryana, Haryana-123031, India.
Praveen Agarwal
- Department of Mathematics, Anand International College of Engineering, Jaipur, Rajasthan, India.
Serkan Araci
- Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410, Gaziantep, Turkey.
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., \(\textbf{450}\) (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.
Share and Cite
ISRP Style
Arun Kajla, Praveen Agarwal, Serkan Araci, A Kantorovich variant of a generalized Bernstein operators, Journal of Mathematics and Computer Science, 19 (2019), no. 2, 86--96
AMA Style
Kajla Arun, Agarwal Praveen, Araci Serkan, A Kantorovich variant of a generalized Bernstein operators. J Math Comput SCI-JM. (2019); 19(2):86--96
Chicago/Turabian Style
Kajla, Arun, Agarwal, Praveen, Araci, Serkan. "A Kantorovich variant of a generalized Bernstein operators." Journal of Mathematics and Computer Science, 19, no. 2 (2019): 86--96
Keywords
- Global approximation
- rate of convergence
- modulus of continuity
- A-statistical convergence
- Kantorovich operators
MSC
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