A Voronovskaja-type formula for the \(q\)-Meyer-König and Zeller operators

Authors

  • Tiberiu Trif Babeş-Bolyai University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat401-953

Keywords:

Meyer-König and Zeller operators, rate of convergence, \(q\)-calculus
Abstract views: 236

Abstract

A Voronovskaja-type formula for the \(q\)-Meyer-König and Zeller operators is presented.

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References

Alkemade, J. A. H., The second moment for the Meyer-König and Zeller operators, J. Approx. Theory, 40, pp. 261-273, 1984. https://doi.org/10.1016/0021-9045(84)90067-4 DOI: https://doi.org/10.1016/0021-9045(84)90067-4

Andrews, G. E., Askey R. and Roy, R., Special Functions, Cambridge University Press, Cambridge, 1999. DOI: https://doi.org/10.1017/CBO9781107325937

Becker, M.and Nessel, R. J., A global approximation theorem for Meyer-K onig and Zeller operators, Math. Z, 160, pp. 195-206, 1978. https://doi.org/10.1007/bf01237033 DOI: https://doi.org/10.1007/BF01237033

Cheney, E. W. and Sharma, A. Bernstein power series, Canad. J. Math., 16, pp. 241-253, 1964. https://doi.org/10.4153/cjm-1964-023-1 DOI: https://doi.org/10.4153/CJM-1964-023-1

Doğru, O. and Duman, O., Statistical approximation of Meyer-König and Zeller operators based on q-integers, Publ. Math. Debrecen, 68, pp. 199-214, 2006. DOI: https://doi.org/10.5486/PMD.2006.3306

Doğru, O. and Gupta, V. Korovkin-type approximation properties of bivariate q-Meyer-König and Zeller operators, Calcolo, 43, pp. 51-63, 2006. https://doi.org/10.1007/s10092-006-0114-8 DOI: https://doi.org/10.1007/s10092-006-0114-8

Doğru, O. and Örkcu, M., King type modification of Meyer-König and Zeller operators based on the q-integers, Math. Comput. Modelling, 50, pp. 1245-1251, 2009. https://doi.org/10.1016/j.mcm.2007.12.005 DOI: https://doi.org/10.1016/j.mcm.2009.07.003

Govil, N. K. and Gupta, V., Convergence of q-Meyer-König-Zeller-Durrmeyer operators, Adv. Stud. Contemp. Math. (Kyungshang), 19, pp. 97-108, 2009.

Lupaş, L., A q-analogue of the Meyer-K onig and Zeller operator, An. Univ. Oradea Fasc. Mat., 2, pp. 62-66, 1992.

Mahmudov, N. I., Korovkin-type theorems and applications, Cent. Eur. J. Math., 7, pp. 348-356, 2009. https://doi.org/10.2478/s11533-009-0006-7 DOI: https://doi.org/10.2478/s11533-009-0006-7

Mamedov, R. G., Asymptotic approximation of differentiable functions by linear positive operators, Dokl. Akad. Nauk SSSR, 128, pp. 471-474, 1959.

Meyer-Konig, W. and Zeller, K., Bernsteinsche Potenzreihen, Studia Math., 19, pp. 89-94, 1960. https://doi.org/10.4064/sm-19-1-89-94 DOI: https://doi.org/10.4064/sm-19-1-89-94

Ostrovska, S., On the improvement of analytic properties under the limit q-Bernstein operator, J. Approx. Theory, 138, pp. 37-53, 2006. https://doi.org/10.1016/j.jat.2005.09.015 DOI: https://doi.org/10.1016/j.jat.2005.09.015

Ostrovska, S., The unicity theorems for the limit q-Bernstein operator, Applicable Anal., 68, pp. 161-167, 2009. https://doi.org/10.1080/00036810802713784 DOI: https://doi.org/10.1080/00036810802713784

Özarslan, M. A. and Duman, O., Approximation theorems by Meyer-König and Zeller type operators, Chaos, Solitons and Fractals, 41, pp. 451-456, 2009. https://doi.org/10.1016/j.chaos.2008.02.006 DOI: https://doi.org/10.1016/j.chaos.2008.02.006

Sharma, H., Properties of q-Meyer-König-Zeller Durrmeyer operators, JIPAM. J. Inequal. Pure Appl. Math., 10, no. 4, Article 105, 10 pp. (electronic), 2009.

Sikkema, P. C., On some linear positive operators, Indag. Math, 32, pp. 327-337, 1970. https://doi.org/10.1016/s1385-7258(70)80037-3 DOI: https://doi.org/10.1016/S1385-7258(70)80037-3

Sikkema, P. C., On the asymptotic approximation with operators of Meyer-König and Zeller, Indag. Math., 32, pp. 428-440, 1970. https://doi.org/10.1016/s1385-7258(70)80047-6 DOI: https://doi.org/10.1016/S1385-7258(70)80047-6

Trif, T., Meyer-König and Zeller operators based on the q-integers, Rev. Anal. Num er. Th eor. Approx., 29, pp. 221-229, 2000, http://ictp.acad.ro/jnaat/journal/article/view/2000-vol29-no2-art13

Wang, H., Korovkin-type theorem and application, J. Approx. Theory, 132, pp. 258-264, 2005. https://doi.org/10.1016/j.jat.2004.12.010 DOI: https://doi.org/10.1016/j.jat.2004.12.010

Wang, H., Properties of convergence for the q-Meyer-K onig and Zeller operators, J. Math. Anal. Appl., 335, pp. 1360-1373, 2007. https://doi.org/10.1016/j.jmaa.2007.01.103 DOI: https://doi.org/10.1016/j.jmaa.2007.01.103

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Published

2011-02-01

How to Cite

Trif, T. (2011). A Voronovskaja-type formula for the \(q\)-Meyer-König and Zeller operators. Rev. Anal. Numér. Théor. Approx., 40(1), 80–89. https://doi.org/10.33993/jnaat401-953

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Vol. 40 No. 1 (2011)

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