Abstract
The present paper deals with the rate of convergence of the general class of Durrmeyer operators, which are generalization of Ibragimov-Gadjiev operators. The special cases of the operators include somewell known operators as particular cases viz. Szász-Mirakyan-Durrmeyer operators, Baskakov-Durrmeyer operators. Herewe estimate the rate of convergence of Ibragimov-Gadjiev-Durrmeyer operators for functions having derivatives of bounded variation.
References
[1] Aral A., Acar T., Modern mathematical methods and high performance computing in science and technology, 1-15, Springer Proc. Math. Stat., 171, (Springer, Singapore, 2016)10.1007/978-981-10-1454-3_1Search in Google Scholar
[2] Gadjiev A. D., Ibragimov I. I., Soviet Math. Dokl., 1970, 11, 1092-1095.Search in Google Scholar
[3] Ulusoy G., Deniz E., Aral A., Appl. Math. Comput., 2015, 260, 126-134.10.1016/j.amc.2015.03.060Search in Google Scholar
[4] Heilmann M., Approx. Theory and Its Appl., 1988, 5(1), 105-127.Search in Google Scholar
[5] Zeng X. M., J. Math. Anal. Appl., 1998, 226, 309-325.10.1006/jmaa.1998.6063Search in Google Scholar
[6] Zeng X. M., Cheng X., J. Comput. Anal. and Appl., 2007, 9(4), 421-430.Search in Google Scholar
[7] Zeng X. M., Tao W., Kyungpook Math. J., 2003, 43, 593-604.Search in Google Scholar
[8] Acar T., Proc. Jangjeon Math. Soc., 2013, 16(1), 21-35.10.4169/mathhorizons.21.1.bmSearch in Google Scholar
[9] Acar T., Gupta V., and Aral A., Bull. Math. Sci., 2011, 1(1), 99-113.10.1007/s13373-011-0005-4Search in Google Scholar
[10] Acar T., Mishra L. N. and Mishra V. N., J. Funct. Spaces, 2015, Art. ID 936308.10.1155/2015/936308Search in Google Scholar
[11] Sinha J., Singh V. K., General Math., 2006, 14(4), 29-36.10.1080/10724117.2006.11974665Search in Google Scholar
[12] Verma D. K., Agrawal P. N., Math. Sci., 2012, 6(22), Art. 22, 8 pp.10.1186/2251-7456-6-22Search in Google Scholar
[13] Gupta V., Agarwal R. P., Convergence Estimates in Approximation Theory, (Springer, 2014)10.1007/978-3-319-02765-4Search in Google Scholar
© 2017 Tuncer Acar
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.