Bivariate Bernstein–Schurer–Stancu type GBS operators in $(p,q)$-analogue

Mursaleen, M.; Ahasan, Mohd.; Ansari, Khursheed J.

doi:10.1186/s13662-020-02547-7

Cited by 6 publications

(2 citation statements)

References 26 publications

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“…İspir [33] established quantitative estimates for the GBS of the Chlodowsky-Szász-kind operators. Recently, some authors introduced the GBS operators of various operators (we refer the readers to [34][35][36][37][38][39][40][41][42]).…”

Section: Construction Of the Gbs Type Of F R 1 R 2 ðμ ; X Yþmentioning

confidence: 99%

Approximation by One and Two Variables of the Bernstein-Schurer-Type Operators and Associated GBS Operators on Symmetrical Mobile Interval

Aslan

Izgi

2021

Journal of Function Spaces

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In this article, we purpose to study some approximation properties of the one and two variables of the Bernstein-Schurer-type operators and associated GBS (Generalized Boolean Sum) operators on a symmetrical mobile interval. Firstly, we define the univariate Bernstein-Schurer-type operators and obtain some preliminary results such as moments, central moments, in connection with a modulus of continuity, the degree of convergence, and Korovkin-type approximation theorem. Also, we derive the Voronovskaya-type asymptotic theorem. Further, we construct the bivariate of this newly defined operator, discuss the order of convergence with regard to Peetre’s K -functional, and obtain the Voronovskaya-type asymptotic theorem. In addition, we consider the associated GBS-type operators and estimate the order of approximation with the aid of mixed modulus of smoothness. Finally, with the help of the Maple software, we present the comparisons of the convergence of the bivariate Bernstein-Schurer-type and associated GBS operators to certain functions with some graphical illustrations and error estimation tables.

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Section: Construction Of the Gbs Type Of F R 1 R 2 ðμ ; X Yþmentioning

confidence: 99%

Approximation by One and Two Variables of the Bernstein-Schurer-Type Operators and Associated GBS Operators on Symmetrical Mobile Interval

Aslan

Izgi

2021

Journal of Function Spaces

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“…For more study we can see [9,30,40,42,46]. If p = 1, the operators (3) reduce to Phillips q-Bernstein operators.…”

Section: Introductionmentioning

confidence: 99%

Approximation by using the Meyer-König and Zeller operators based on (p,q)-analogue

Kadak

Khan

Mursaleen

2021

Filomat

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In this paper, a generalization of the q-Meyer-K?nig and Zeller operators by means of the (p,q)- calculus is introduced. Some approximation results for (p,q)-analogue of Meyer-K?nig and Zeller operators denoted by Mn,p,q for 0 < q < p ? 1 are obtained. Also we investigate classical and statistical versions of Korovkin type approximation results based on proposed operator. Furthermore, some graphical examples for convergence of the operators are presented.

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Approximation properties for the genuine modified Bernstein-Durrmeyer-Stancu operators

Cai

Kantar

Çekіm

2020

Appl. Math. J. Chin. Univ.

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Bivariate Bernstein–Schurer–Stancu type GBS operators in $(p,q)$-analogue

Cited by 6 publications

References 26 publications

Approximation by One and Two Variables of the Bernstein-Schurer-Type Operators and Associated GBS Operators on Symmetrical Mobile Interval

Approximation by One and Two Variables of the Bernstein-Schurer-Type Operators and Associated GBS Operators on Symmetrical Mobile Interval

Approximation by using the Meyer-König and Zeller operators based on (p,q)-analogue

Approximation properties for the genuine modified Bernstein-Durrmeyer-Stancu operators

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