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

Vijay Gupta; Michael Th. Rassias

doi:10.33993/jnaat502-1235

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

DOI:

https://doi.org/10.33993/jnaat502-1235

Keywords:

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

Abstract views: 219

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