A Kantorovich variant of a generalized Bernstein operators

Volume 19, Issue 2, pp 86--96 http://dx.doi.org/10.22436/jmcs.019.02.03
Publication Date: May 03, 2019 Submission Date: November 21, 2017 Revision Date: May 11, 2018 Accteptance Date: April 01, 2019

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.


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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


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