The moments for the Meyer–König and Zeller operators

Guo, Shuangjian; Qi, Qiulan

doi:10.1016/j.aml.2006.09.002

Cited by 11 publications

(3 citation statements)

References 3 publications

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“…[1-3, 5, 6, 8, 9, 11-16]). Recently, S. Guo and Q. Qi in [8] proved that for every q ∈ N there exists a positive constant K(q) dependent only on q (independent on x and n) such that for A n;q (x) =:…”

Section: 2mentioning

confidence: 99%

Approximation by generalized MKZ-operators in polynomial weighted spaces

Rempulska

Skorupka

2007

Analys in Theo Applic

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Section: 2mentioning

confidence: 99%

Approximation by generalized MKZ-operators in polynomial weighted spaces

Rempulska

Skorupka

2007

Analys in Theo Applic

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“…It is difficult to get the estimates of the moments for the Meyer-König and Zeller type operators (cf. [2], [3], [10]). The direct and inverse results for Durrmeyer-type modifications of the Meyer-König and Zeller operators are not perfect.…”

Section: Introductionmentioning

confidence: 99%

Pointwise approximation theorems for Meyer--König and Zeller--Durrmeyer operators

Qi¹,

Liu²

2008

Publ. Math. Debrecen

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“…Abel [2] derived the estimates of r-order moments for Meyer-König and Zeller operators, but due to the complicated expression of these operators, their central moments were not given. Recently, Guo et al [3] gave the estimates of 2p-order central moments for and Mahmudov [4] gave the estimates of m-order central moments for qBernstein operators in the case of 0 1 q < < . Based on these estimates, the approximation theorems for these qanalogue of operators and Bernstein operators were proposed [5][6][7][8][9][10][11] .…”

mentioning

confidence: 99%

Estimates of central moments for one kind of exponential-type operators

Song

Yang

2011

Trans. Tianjin Univ.

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Abstract：In this paper, the explicit estimates of central moments for one kind of exponential-type operators are derived. The estimates play an essential role in studying the explicit approximation properties of this family of operators. Using the proposed method, the results of Ditzian and Totik in 1987, Guo and Qi in 2007, and Mahmudov in 2010 can be improved respectively.In 1987, a new natural modulus of smoothness was introduced by Ditzian and Totik [1] for the investigation of exponential-type operators, such as Bernstein operators, Szász operators, Baskakov operators and Post-Widder operators. To investigate the approximation properties of these exponential-type operators or Bernstein-type operators, the estimates of central moments for these types of operators [1] were given firstly. However, the estimates of central moments for Meyer-König and Zeller operators, which belong to five kinds of Bernstein-type operators, are still open. Abel [2] derived the estimates of r-order moments for Meyer-König and Zeller operators, but due to the complicated expression of these operators, their central moments were not given. Recently, Guo et al [3] gave the estimates of 2p-order central moments for and Mahmudov [4] gave the estimates of m-order central moments for qBernstein operators in the case of 0 1 q < < . Based on these estimates, the approximation theorems for these qanalogue of operators and Bernstein operators were proposed [5][6][7][8][9][10][11] . In fact, all of these estimates mentioned above are only rough estimates, the values of constant C appearing in the estimates of upper bound of central moments are still unknown. In this paper, we will give explicit estimates of the central moments for one kind of exponential-type operators, which are connected with Szász operators and Baskakov operators directly, but not connected with Bernstein operators and Meyer-König and Zeller operators.

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The moments for the Meyer–König and Zeller operators

Cited by 11 publications

References 3 publications

Approximation by generalized MKZ-operators in polynomial weighted spaces

Approximation by generalized MKZ-operators in polynomial weighted spaces

Pointwise approximation theorems for Meyer--König and Zeller--Durrmeyer operators

Estimates of central moments for one kind of exponential-type operators

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