Some approximation properties of q-Durrmeyer operators

Gupta, Vijay

doi:10.1016/j.amc.2007.07.056

Cited by 119 publications

(56 citation statements)

References 8 publications

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“…Clearly, for p > 1, ( p, q)-Bernstein Durrmeyer operators coincide with q-Bernstein Durrmeyer operators [12].…”

Section: By Using Identitymentioning

confidence: 99%

On Durrmeyer-type generalization of (p, q)-Bernstein operators

Sharma

2016

Arab. J. Math.

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In this paper, we introduce ( p, q)-Bernstein Durrmeyer operators. We define ( p, q)-beta integral and use it to obtain the moments of the operators. We obtain uniform convergence of the operators by using Korovkin's theorem. We estimate direct results of the operators by means of modulus of continuity and Peetre K -functional. Finally, we find Voronovskaya-type theorem for the operators. Mathematics Subject Classification 41A25 · 41A35

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“…Clearly, for p > 1, ( p, q)-Bernstein Durrmeyer operators coincide with q-Bernstein Durrmeyer operators [12].…”

Section: By Using Identitymentioning

confidence: 99%

On Durrmeyer-type generalization of (p, q)-Bernstein operators

Sharma

2016

Arab. J. Math.

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“…Some approximation properties of these operators were studied by Gupta and Srivastava [16] and by May [24]. Recently, Gupta [10] introduced and studied approximation properties of q-Durrmeyer operators. Gupta and Heping [15] introduced the q-Durrmeyer type operators and studied estimation of the rate of convergence for continuous functions in terms of modulus of continuity.…”

Section: Introductionmentioning

confidence: 99%

Weighted approximation properties of Stancu type modification of q-Szász-Durrmeyer operators

İçöz¹

2016

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…In order to prove some approximation properties of the GBS q -Durrmeyer operators, we need the following result obtained by Gupta in [19].…”

Section: A Convergence Theorem For the Sequence U Mnq1q2mentioning

confidence: 99%

On certain GBS-Durrmeyer operators based on $q$-integers

Bărbosu¹,

Acu²,

Muraru³

2017

Turk J Math

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In the present paper we introduce the GBS (Generalized Boolean Sum) operators of Durrmeyer type based on q -integers and the approximation of B-continuous functions using the above operators is studied. In addition, a uniform convergence theorem is established and the degree of approximation in terms of mixed modulus of continuity is evaluated. The study contains in the last section numerical considerations regarding the constructed operators based on MATLAB algorithms.

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Some approximation properties of q-Durrmeyer operators

Cited by 119 publications

References 8 publications

On Durrmeyer-type generalization of (p, q)-Bernstein operators

On Durrmeyer-type generalization of (p, q)-Bernstein operators

Weighted approximation properties of Stancu type modification of q-Szász-Durrmeyer operators

On certain GBS-Durrmeyer operators based on $q$-integers

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