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Approximation by Complex Meyer-König and Zeller Operators
School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, China
School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, China
- 1 School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, China
- 2 School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, China
Advances in Pure Mathematics·Volume 10 (2020)·Pages 1–11·Published 7 January 2020·DOI10.4236/apm.2020.101001
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Abstract
The Meyer-K ö nig and Zeller operator is one of the most challenging operators. Sometimes the study of its properties will rely on the weighted approximation by Baskakov operator. In this paper, this relation is extended to complex space; the quantitative estimates and the Voronovskaja type results for analytic functions by complex Meyer-K ö nig and Zeller operators were obtained.
KeywordsComplex Meyer-König and Zeller OperatorsComplex Baskakov OperatorsVoronovskaja Type ResultAnalytic Function
- Becker, M. and Nessel, R.J. (1978) A Global Approximation Theorem for Meyer-König and Zeller Operators. Mathematische Zeitschrift, 160, 195-206. https://doi.org/10.1007/BF01237033
- Totik, V. (1983) Uniform Approximation by Baskakov and Meyer-König and Zeller Operators. Periodica Mathematica Hungarica, 14, 209-228. https://doi.org/10.1007/BF01849019
- Abel, U. (1995) The Moments for the Meyer-König and Zeller Operators. Journal of Approximation Theory, 82, 352-361. https://doi.org/10.1006/jath.1995.1084
- Chen, W. (1986) On the Integral Type Meyer-König and Zeller Operators. Approximation Theory and Its Applications, 2, 7-18.
- Guo, S.S. and Qi, Q.L. (2007) The Moments for the Meyer-König and Zeller Operators. Applied Mathematics Letters, 20, 719-722. https://doi.org/10.1016/j.aml.2006.09.002
- Gadjev, I. (2015) Strong Converse Result for Uniform Approximation by Meyer-König and Zeller Operators. Journal of Mathematical Analysis and Applications, 428, 32-42. https://doi.org/10.1016/j.jmaa.2015.03.004
- Ivanov, K.G. and Parvanov, P.E. (2012) Weighted Approximation by Meyer-König and Zeller Operators. In: Nikolov, G. and Uluchev, R., Eds., Constructive Theory of Functions, Sozopol 2010, Academic Publishing House, Sofia, 150-160.
- Heilmann, M. (2003) Commutativity of Durrmeyer-Type Modifications of Meyer-König and Zeller and Baskakov Operators. In: Bojanov, B.D., Ed., Constructive Theory of Functions, Varna 2002, Darba, Sofia, 295-301.
- Heilmann, M. (2003) Eigenfunctions of Durrmeyer-Type Modifications of Meyer-König and Zeller and Baskakov Operators. Journal of Approximation Theory, 125, 63-73. https://doi.org/10.1016/j.jat.2003.09.006
- Abel, U., Gupta, V. and Ivav, M. (2004) The Complete Asymptotic Expansion for a General Durrmeyer Variant of the Meyer-König and Zeller Operators. Mathematical and Computer Modelling, 40, 867-875. https://doi.org/10.1016/j.mcm.2004.10.016
- Heilmann, M. (2006) Eigenfunctions and Eigenvalues for Some Durrmeyer-Type Operators. In: Bojanov, B.D., Ed., Constructive Theory of Functions, Varna 2005, Academic Publishing House, Sofia, 158-167.
- Harun, K. (2017) Approximation by Urysohn Type Meyer-König and Zeller Operators to Urysohn Integral Operators. Results in Mathematics, 72, 1571-1583. https://doi.org/10.1007/s00025-017-0729-x
- Mehmet, A. (2016) New Korovkin Type Theorem for Non-Tensor Meyer-König and Zeller Operators. Results in Mathematics, 69, 327-343. https://doi.org/10.1007/s00025-015-0472-0