Asymptotic formula in simultaneous approximation for certain Ismail-May-Baskakov operators

Authors

  • Vijay Gupta Department of Mathematics, Netaji Subhas Institute of Technology, New Delhi, India
  • Michael Th. Rassias Department of Mathematics and Engineering Sciences, Hellenic Military Academy, Greece and Institute for Advanced Study, Program in Interdisciplinary Studies, Princeton, USA

Keywords:

Approximation Theory, Ismail-May operators, Baskakov basis, asymptotic formula, simultaneous approximation, weighted Korovkin's theorem

Abstract

In the present paper, we introduce a modification of Ismail-May operators having weights of Baskakov basis functions. We estimate weighted Korovkin's theorem and difference estimates between two operators and establish a Voronovskaja type asymptotic formula in simultaneous approximation.

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References

A. M. Acu and I. Rasa,New estimates for the differences of positive linear operators,Numer. Algor.73(2016), pp. 775-789, https://doi.org.10.1007/s11075-016-0117-8

O. Agratini, Approximation properties of a family of integral type operators, Positivity 25(2021) no. 1, pp. 97-108, https://doi.org.10.1007/s11117-020-00752-y

P. N. Agrawal and K. J. Thamer, Approximation of unbounded functions by a newsequence of linear positive operators, J. Math. Anal. Appl.225 (1998), pp. 660-672, https://doi.org.10.1006/jmaa.1998.6036

A. D. Gadjiev, Theorems of Korovkin type, Math. Zametki 20(1976), no. 5, pp. 781-786.

V. Gupta, General estimates for the difference of operators, Comp. Math. Methods, 1 (2019): e1018, pp. 1-12, https://doi.org.doi.org/10.1002/cmm4.1018

V. Gupta and G. Agrawal, Approximation for link Ismail-May operators, Ann. Funct. Anal. 11 (2020), pp. 728-747, https://doi.org.10.1007/s43034-019-00051-y

V. Gupta and G. C. Greubel, Moment estimations of new Szasz-Mirakyan-Durrmeyer operators, Appl. Math. Comput.271(2015), pp. 540-547, https://doi.org.10.1016/j.amc.2015.09.037

V. Gupta and M. A. Noor, Convergence of derivatives for certain mixed Szasz–Beta operators, J. Math. Anal. Appl.321(2006) no. 1, pp. 1-9, https://doi.org.10.1016/j.jmaa.2005.07.036

V. Gupta and Th. M. Rassias, Direct estimates for certain Szasz type operators, Appl. Math. Comput. 251 (2015), pp. 469-474, https://doi.org.10.1016/j.amc.2014.11.078

V. Gupta and M. Th. Rassias, Moments of Linear Positive Operators and Approxi-mation, Series: Springer Briefs in Mathematics, Springer Nature Switzerland AG (2019), https://doi.org.10.1007/978-3-030-19455-0

V. Gupta, D. K. Verma and P. N. Agrawal, Simultaneous approximation by certain Baskakov-Durrmeyer-Stancu operators, J. Egyptian Math. Soc. 20 (2012) no. 3, pp.183-187, https://doi.org.10.1016/j.joems.2012.07.001

M. Ismail, Polynomials of binomial type and approximation theory, J. Approx. Theory 23 (1978), pp. 177-186, https://doi.org.10.1016/0021-9045(78)90105-3

M. Ismail and C. P. May, On a family of approximation operators, J. Math. Anal. Appl. 63 (1978), pp. 446-462, https://doi.org.10.1016/0022-247X(78)90090-2

N. Ispir, On modified Baskakov operators on weighted spaces, Turk. J. Math. 26 (2001) no. 3, pp. 355-365

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Published

2021-12-31

How to Cite

Gupta, V., & Rassias, M. T. (2021). Asymptotic formula in simultaneous approximation for certain Ismail-May-Baskakov operators. J. Numer. Anal. Approx. Theory, 50(2), 153–163. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1235

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