An Improved Estimate of the Rate of Convergence of the Integrated Meyer-König and Zeller Operators for Functions of Bounded Variation

Love, E. R.; Prasad, Govind; Sahai, Ashok

doi:10.1006/jmaa.1994.1341

Cited by 11 publications

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“…Lemma 2.2 [7]. If {ξ i }, i = 1, 2, 3,..., are independent random variables with the same geometric distribution…”

Section: Auxiliary Resultsmentioning

confidence: 99%

“…Lemma 2.1 [7]. Let X 1 ,X 2 ,X 3 ,...,X n be n independent and identically distributed random variables with zero mean and a finite absolute third moment.…”

Section: Auxiliary Resultsmentioning

confidence: 99%

“…The rates of convergence of some integral modifications of operators (1.1) were discussed in [2,4,5,6,7,10]. Guo [1] introduced Meyer-König and Zeller operators aŝ…”

Section: Introduction For a Function Defined On [0mentioning

confidence: 99%

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A note on integral modification of the Meyer‐König and Zeller operators

Gupta

Kumar

2003

International Journal of Mathematics and Mathematical Sciences

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Guo (1988) introduced the integral modification of Meyer-König and Zeller operatorsM n and studied the rate of convergence for functions of bounded variation. Gupta (1995) gave the sharp estimate for the operatorsM n . Zeng (1998) gave the exact bound and claimed to improve the results of Guo and Gupta, but there is a major mistake in the paper of Zeng. In the present note, we give the correct estimate for the rate of convergence on bounded variation functions.2000 Mathematics Subject Classification: 41A30, 41A36.

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“…Lemma 2.2 [7]. If {ξ i }, i = 1, 2, 3,..., are independent random variables with the same geometric distribution…”

Section: Auxiliary Resultsmentioning

confidence: 99%

“…Lemma 2.1 [7]. Let X 1 ,X 2 ,X 3 ,...,X n be n independent and identically distributed random variables with zero mean and a finite absolute third moment.…”

Section: Auxiliary Resultsmentioning

confidence: 99%

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A note on integral modification of the Meyer‐König and Zeller operators

Gupta

Kumar

2003

International Journal of Mathematics and Mathematical Sciences

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“…The rate of convergence for the Kantorovitch type modification of the operators M n on functions of bounded variation was initially studied by Guo [4]. Several other corrections and improvements of the Guo's [4] work can be found in [6,7,9,12] etc. Recently, Zeng [13] estimated the rate of convergence of the Bézier variant of the Meyer-Konig and Zeller operators and its Kantorovitch modification.…”

Section: Introductionmentioning

confidence: 98%

Degree of approximation to function of bounded variation by Bézier variant of MKZ operators

Gupta

2004

Journal of Mathematical Analysis and Applications

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Guo (Approx. Theory Appl. 4 (1988) 9-18) introduced the integral modification of Meyer-Konig and Zeller operatorsM n and studied the rate of convergence for functions of bounded variation. In this paper we introduce the Bézier variant of these integrated MKZ operators and study the rate of convergence by means of the decomposition technique of functions of bounded variation together with some results of probability theory and the exact bound of MKZ basis functions. Recently, Zeng (J. Math. Anal. Appl. 219 (1998) 364-376) claimed to improve the results of Guo and Gupta (Approx. Theory Appl. 11 (1995) 106-107), but there is a major mistake in the paper of Zeng. For special case our main theorem gives the correct estimate on the rate of convergence, over the result of Zeng.

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On a Special Property of the Averaged Modulus for Functions of Bounded Variation

Lenze

1999

New Developments in Approximation Theory

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An Improved Estimate of the Rate of Convergence of the Integrated Meyer-König and Zeller Operators for Functions of Bounded Variation

Cited by 11 publications

References 0 publications

A note on integral modification of the Meyer‐König and Zeller operators

A note on integral modification of the Meyer‐König and Zeller operators

Degree of approximation to function of bounded variation by Bézier variant of MKZ operators

On a Special Property of the Averaged Modulus for Functions of Bounded Variation

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