Approximation Properties of Bivariate Extension of q-Bernstein–Schurer–Kantorovich operators

Acu, Ana Maria; Muraru, Carmen Violeta

doi:10.1007/s00025-015-0441-7

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Introduction3

The Construction Of the Modified Bernstein-stancu Operators1

Competing Interests1

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Cited by 17 publications

(9 citation statements)

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“…Agrawal, Z. Finta and A. Sathish Kumar [15], [7], G. Nowak and V. Gupta [21], A.M. Acu, C.V. Muraru, D. Bȃrbosu and D.F. Sofonea [2], [4] and [3].…”

Section: The Construction Of the Modified Bernstein-stancu Operatorsmentioning

confidence: 99%

Quantitative estimates for some modified Bernstein-Stancu operators

Radu¹

2018

MMN

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“…Agrawal, Z. Finta and A. Sathish Kumar [15], [7], G. Nowak and V. Gupta [21], A.M. Acu, C.V. Muraru, D. Bȃrbosu and D.F. Sofonea [2], [4] and [3].…”

Section: The Construction Of the Modified Bernstein-stancu Operatorsmentioning

confidence: 99%

Quantitative estimates for some modified Bernstein-Stancu operators

Radu¹

2018

MMN

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“…4 Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, 60800, Pakistan. 5 Department of Mathematics, Dong-A University, Busan, 49315, Korea.…”

Section: Competing Interestsmentioning

confidence: 99%

Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators

et al. 2016

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This paper is concerned with the (p, q)-analog of Bernstein operators. It is proved that, when the function is convex, the (p, q)-Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that verify these properties are considered. A global approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem are proved. MSC: 41A10; 41A25; 41A35

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“…The Kantorvich modifications of some wellknown operators in q-calculus were extensively studied in the last decades. We refer the readers to Acu and Muraru (2015) and Agrawal et al (2015). In this paper, we propose to introduce Kantorovich type generalization of (p, q)-Bernstein operators for bivariate functions.…”

Section: Introductionmentioning

confidence: 99%

Approximation by Bivariate (p, q)-Bernstein–Kantorovich Operators

Acar

Aral

Mohiuddine

2016

Iran J Sci Technol Trans Sci

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In the present paper, we introduce Kantorovich modifications of (p, q)-Bernstein operators for bivariate functions using a new (p, q)-integral. We first estimate the moments and central moments. We give the uniform convergence of new operators, rate of convergence in terms of modulus of continuity. The approximations behaviours of the operators for functions having continuous partial derivatives and for functions belong to Lipschitz class are investigated as well.

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Approximation Properties of Bivariate Extension of q-Bernstein–Schurer–Kantorovich operators

Cited by 17 publications

References 11 publications

Quantitative estimates for some modified Bernstein-Stancu operators

Quantitative estimates for some modified Bernstein-Stancu operators

Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators

Approximation by Bivariate (p, q)-Bernstein–Kantorovich Operators

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