Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators

We construct the bivariate form of Bernstein–Schurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K -functional of our newly defined operators. Moreover, we define the associated generalized B...

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Veröffentlicht in:Advances in difference equations Jg. 2020; H. 1; S. 1 - 17
1. Verfasser: Mohiuddine, S. A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.12.2020
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Abstract We construct the bivariate form of Bernstein–Schurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K -functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.
AbstractList We construct the bivariate form of Bernstein–Schurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K -functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.
We construct the bivariate form of Bernstein–Schurer operators based on parameter α. We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K-functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.
Abstract We construct the bivariate form of Bernstein–Schurer operators based on parameter α. We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K-functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.
ArticleNumber 676
Author Mohiuddine, S. A.
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  surname: Mohiuddine
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  organization: Department of General Required Courses, Mathematics, Faculty of Applied Studies, King Abdulaziz University, Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University
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Cites_doi 10.1186/s13660-018-1909-2
10.1007/978-3-662-02888-9
10.1007/s40995-020-00914-3
10.1007/s40995-020-01018-8
10.1017/S0004972700004494
10.1007/s13398-018-0591-z
10.1007/s00025-018-0838-1
10.1186/s13660-018-1653-7
10.1007/s40995-020-01024-w
10.1186/s13662-020-02925-1
10.2298/FIL1911473O
10.1007/s40995-016-0045-4
10.1186/s13660-016-1045-9
10.1007/s11785-016-0633-5
10.1007/978-1-4612-1360-4
10.1186/s13660-018-1688-9
10.1007/s00025-018-0773-1
10.1007/s13398-020-00802-w
10.1186/s13660-018-1693-z
10.1007/s11785-016-0572-1
10.3390/sym11030316
10.1007/s00025-018-0789-6
10.1186/s13660-019-2055-1
10.1080/01630563.2015.1056914
10.1016/j.jmaa.2016.12.075
10.2298/FIL1914549M
10.1080/03081079.2019.1608985
10.5269/bspm.v37i4.35852
10.1007/s40995-017-0433-4
10.1002/mma.4559
10.1007/s13398-020-00903-6
10.1002/mma.5762
10.1016/j.amc.2013.11.095
10.1515/crll.1934.170.197
10.1016/j.amc.2013.03.115
10.37193/CMI.2013.01.09
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Issue 1
Keywords Bernstein operators
Bögel differentiable function
41A25
41A36
Bivariate
GBS operators
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Bernstein–Schurer operators
Modulus of continuity
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References Kajla, Mohiuddine, Alotaibi, Goyal, Singh (CR23) 2020; 44
Nasiruzzaman (CR35) 2020
Srivastava, Özger, Mohiuddine (CR42) 2019; 11
Anastassiou, Gal (CR5) 2000
Badea, Badea, Cottin, Gonska (CR7) 1988; 4
Devore, Lorentz (CR18) 1993
Mursaleen, Khan, Khan (CR34) 2015; 36
Mohiuddine, Acar, Alotaibi (CR26) 2017; 40
Acar, Aral, Mohiuddine (CR1) 2016; 2016
Mohiuddine, Alamri (CR28) 2019; 113
Mohiuddine, Özger (CR32) 2020; 114
Aral, Erbay (CR6) 2019; 24
CR11
İlarslan, Erbay, Aral (CR20) 2019; 42
Belen, Mohiuddine (CR10) 2013; 219
Rao, Nasiruzamman (CR40) 2018; 2018
Badea, Badea, Gonska (CR8) 1986; 34
Dobrescu, Matei (CR19) 1966; 4
Volkov (CR43) 1957; 115
Acar, Kajla (CR3) 2018; 73
Mohiuddine, Ahmad, Özger, Alotaibi, Hazarika (CR27) 2020
Mohiuddine, Hazarika, Alghamdi (CR30) 2019; 33
Kajla, Miclăuş (CR22) 2018; 73
Bögel (CR12) 1934; 170
Mohiuddine, Acar, Alghamdi (CR25) 2018; 2018
Acar, Aral, Mohiuddine (CR2) 2018; 42
Özger, Srivastava, Mohiuddine (CR38) 2020; 114
Chen, Tan, Liu, Xie (CR17) 2017; 450
Kadak, Mohiuddine (CR21) 2018; 73
Mohiuddine, Asiri, Hazarika (CR29) 2019; 48
Mursaleen, Ansari, Khan (CR33) 2017; 11
Badea, Cottin (CR9) 1990
Mohiuddine, Kajla, Mursaleen, Alghamdi (CR31) 2020; 2020
Cai (CR15) 2018; 2018
Miclăuş (CR24) 2013; 22
Cai, Lian, Zhou (CR16) 2018; 2018
Wafi, Rao (CR45) 2019; 37
Nasiruzzaman, Rao, Wazir, Kumar (CR36) 2019; 2019
Bögel (CR13) 1962; 65
Özger (CR37) 2019; 33
CR41
Braha, Srivastava, Mohiuddine (CR14) 2014; 228
Pop (CR39) 2007; 14
Acar, Mohiuddine, Mursaleen (CR4) 2018; 12
Wafi, Rao (CR44) 2019; 43
U. Kadak (3125_CR21) 2018; 73
S.A. Mohiuddine (3125_CR29) 2019; 48
A. Aral (3125_CR6) 2019; 24
A. Wafi (3125_CR45) 2019; 37
D. Miclăuş (3125_CR24) 2013; 22
S.A. Mohiuddine (3125_CR30) 2019; 33
O.T. Pop (3125_CR39) 2007; 14
T. Acar (3125_CR1) 2016; 2016
S.A. Mohiuddine (3125_CR31) 2020; 2020
X. Chen (3125_CR17) 2017; 450
M. Nasiruzzaman (3125_CR36) 2019; 2019
3125_CR11
M. Mursaleen (3125_CR33) 2017; 11
R.A. Devore (3125_CR18) 1993
E. Dobrescu (3125_CR19) 1966; 4
T. Acar (3125_CR2) 2018; 42
S.A. Mohiuddine (3125_CR25) 2018; 2018
M. Nasiruzzaman (3125_CR35) 2020
A. Kajla (3125_CR23) 2020; 44
T. Acar (3125_CR3) 2018; 73
H.G.I. İlarslan (3125_CR20) 2019; 42
N. Rao (3125_CR40) 2018; 2018
C. Badea (3125_CR8) 1986; 34
C. Badea (3125_CR9) 1990
A. Kajla (3125_CR22) 2018; 73
F. Özger (3125_CR38) 2020; 114
H.M. Srivastava (3125_CR42) 2019; 11
K. Bögel (3125_CR12) 1934; 170
V.I. Volkov (3125_CR43) 1957; 115
S.A. Mohiuddine (3125_CR32) 2020; 114
N.L. Braha (3125_CR14) 2014; 228
M. Mursaleen (3125_CR34) 2015; 36
G.A. Anastassiou (3125_CR5) 2000
K. Bögel (3125_CR13) 1962; 65
Q.-B. Cai (3125_CR15) 2018; 2018
3125_CR41
Q.-B. Cai (3125_CR16) 2018; 2018
T. Acar (3125_CR4) 2018; 12
A. Wafi (3125_CR44) 2019; 43
S.A. Mohiuddine (3125_CR26) 2017; 40
S.A. Mohiuddine (3125_CR27) 2020
F. Özger (3125_CR37) 2019; 33
C. Badea (3125_CR7) 1988; 4
S.A. Mohiuddine (3125_CR28) 2019; 113
C. Belen (3125_CR10) 2013; 219
References_xml – volume: 2018
  year: 2018
  ident: CR40
  article-title: A generalized Dunkl type modifications of Phillips operators
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-018-1909-2
– year: 1993
  ident: CR18
  publication-title: Constructive Approximation
  doi: 10.1007/978-3-662-02888-9
– volume: 44
  start-page: 1111
  year: 2020
  end-page: 1118
  ident: CR23
  article-title: Approximation by -Baskakov–Durrmeyer-type hybrid operators
  publication-title: Iran. J. Sci. Technol. Trans. A, Sci.
  doi: 10.1007/s40995-020-00914-3
– year: 2020
  ident: CR35
  article-title: Approximation properties by Szász–Mirakjan operators to bivariate functions via Dunkl analogue
  publication-title: Iran. J. Sci. Technol. Trans. A, Sci.
  doi: 10.1007/s40995-020-01018-8
– volume: 24
  start-page: 119
  year: 2019
  end-page: 131
  ident: CR6
  article-title: Parametric generalization of Baskakov operators
  publication-title: Math. Commun.
– start-page: 51
  year: 1990
  end-page: 68
  ident: CR9
  article-title: Korovkin-type theorems for generalized boolean sum operators, approximation theory (Kecskemét, 1900)
  publication-title: Colloq. Math. Soc. János Bolyai
– volume: 228
  start-page: 162
  year: 2014
  end-page: 169
  ident: CR14
  article-title: A Korovkin’s type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean
  publication-title: Appl. Math. Comput.
– volume: 4
  start-page: 95
  year: 1988
  end-page: 108
  ident: CR7
  article-title: Notes on the degree of approximation of -continuous and -differentiable functions
  publication-title: Approx. Theory Appl.
– volume: 34
  start-page: 53
  year: 1986
  end-page: 64
  ident: CR8
  article-title: A test function theorem and approximation by pseudo polynomials
  publication-title: Bull. Aust. Math. Soc.
  doi: 10.1017/S0004972700004494
– volume: 113
  start-page: 1955
  issue: 3
  year: 2019
  end-page: 1973
  ident: CR28
  article-title: Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems
  publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.
  doi: 10.1007/s13398-018-0591-z
– volume: 73
  year: 2018
  ident: CR3
  article-title: Degree of approximation for bivariate generalized Bernstein type operators
  publication-title: Results Math.
  doi: 10.1007/s00025-018-0838-1
– volume: 2018
  year: 2018
  ident: CR16
  article-title: Approximation properties of -Bernstein operators
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-018-1653-7
– volume: 22
  start-page: 73
  year: 2013
  end-page: 80
  ident: CR24
  article-title: On the GBS Bernstein–Stancu’s type operators
  publication-title: Creative Math. Inform.
– year: 2020
  ident: CR27
  article-title: Approximation by the parametric generalization of Baskakov–Kantorovich operators linking with Stancu operators
  publication-title: Iran. J. Sci. Technol. Trans. A, Sci.
  doi: 10.1007/s40995-020-01024-w
– volume: 2020
  year: 2020
  ident: CR31
  article-title: Blending type approximation by -Baskakov–Durrmeyer type hybrid operators
  publication-title: Adv. Differ. Equ.
  doi: 10.1186/s13662-020-02925-1
– volume: 33
  start-page: 3473
  issue: 11
  year: 2019
  end-page: 3486
  ident: CR37
  article-title: Weighted statistical approximation properties of univariate and bivariate -Kantorovich operators
  publication-title: Filomat
  doi: 10.2298/FIL1911473O
– volume: 42
  start-page: 655
  year: 2018
  end-page: 662
  ident: CR2
  article-title: Approximation by bivariate -Bernstein–Kantorovich operators
  publication-title: Iran. J. Sci. Technol. Trans. A, Sci.
  doi: 10.1007/s40995-016-0045-4
– volume: 2016
  year: 2016
  ident: CR1
  article-title: On Kantorovich modification of -Baskakov operators
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-016-1045-9
– volume: 12
  start-page: 1453
  year: 2018
  end-page: 1468
  ident: CR4
  article-title: Approximation by -Baskakov–Durrmeyer–Stancu operators
  publication-title: Complex Anal. Oper. Theory
  doi: 10.1007/s11785-016-0633-5
– year: 2000
  ident: CR5
  publication-title: Approximation Theory: Moduli of Continuity and Global Smoothness Preservation
  doi: 10.1007/978-1-4612-1360-4
– volume: 2018
  year: 2018
  ident: CR15
  article-title: The Bézier variant of Kantorovich type -Bernstein operators
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-018-1688-9
– volume: 73
  issue: 1
  year: 2018
  ident: CR22
  article-title: Blending type approximation by GBS operators of generalized Bernstein–Durrmeyer type
  publication-title: Results Math.
  doi: 10.1007/s00025-018-0773-1
– volume: 114
  year: 2020
  ident: CR32
  article-title: Approximation of functions by Stancu variant of Bernstein–Kantorovich operators based on shape parameter
  publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.
  doi: 10.1007/s13398-020-00802-w
– volume: 2018
  year: 2018
  ident: CR25
  article-title: Genuine modified Bernstein–Durrmeyer operators
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-018-1693-z
– volume: 11
  start-page: 85
  issue: 1
  year: 2017
  end-page: 107
  ident: CR33
  article-title: Approximation by a Kantorovich type -Bernstein–Stancu operators
  publication-title: Complex Anal. Oper. Theory
  doi: 10.1007/s11785-016-0572-1
– volume: 11
  issue: 3
  year: 2019
  ident: CR42
  article-title: Construction of Stancu-type Bernstein operators based on Bézier bases with shape parameter
  publication-title: Symmetry
  doi: 10.3390/sym11030316
– volume: 4
  start-page: 85
  year: 1966
  end-page: 90
  ident: CR19
  article-title: The approximation by Bernstein type polynomials of bidimensional continuous functions
  publication-title: An. Univ. Timişoara Ser. Şti. Mat.-Fiz.
– volume: 65
  start-page: 45
  year: 1962
  end-page: 71
  ident: CR13
  article-title: Über die mehrdimensionale differentiation
  publication-title: Jahresber. Dtsch. Math.-Ver.
– volume: 219
  start-page: 9821
  year: 2013
  end-page: 9826
  ident: CR10
  article-title: Generalized weighted statistical convergence and application
  publication-title: Appl. Math. Comput.
– volume: 73
  year: 2018
  ident: CR21
  article-title: Generalized statistically almost convergence based on the difference operator which includes the -gamma function and related approximation theorems
  publication-title: Results Math.
  doi: 10.1007/s00025-018-0789-6
– volume: 2019
  year: 2019
  ident: CR36
  article-title: Approximation on parametric extension of Baskakov–Durrmeyer operators on weighted spaces
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-019-2055-1
– ident: CR11
– volume: 36
  start-page: 1178
  issue: 9
  year: 2015
  end-page: 1197
  ident: CR34
  article-title: Approximation properties for modified -Bernstein–Kantorovich operators
  publication-title: Numer. Funct. Anal. Optim.
  doi: 10.1080/01630563.2015.1056914
– volume: 450
  start-page: 244
  year: 2017
  end-page: 261
  ident: CR17
  article-title: Approximation of functions by a new family of generalized Bernstein operators
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2016.12.075
– volume: 33
  start-page: 4549
  issue: 14
  year: 2019
  end-page: 4560
  ident: CR30
  article-title: Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems
  publication-title: Filomat
  doi: 10.2298/FIL1914549M
– volume: 14
  start-page: 15
  year: 2007
  end-page: 31
  ident: CR39
  article-title: Approximation of -differentiable functions by GBS operators
  publication-title: An. Univ. Oradea, Fasc. Mat.
– volume: 48
  start-page: 492
  issue: 5
  year: 2019
  end-page: 506
  ident: CR29
  article-title: Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems
  publication-title: Int. J. Gen. Syst.
  doi: 10.1080/03081079.2019.1608985
– volume: 37
  start-page: 137
  issue: 4
  year: 2019
  end-page: 151
  ident: CR45
  article-title: Approximation properties of -variant of Stancu–Schurer operators
  publication-title: Bol. Soc. Parana. Mat.
  doi: 10.5269/bspm.v37i4.35852
– volume: 115
  start-page: 17
  year: 1957
  end-page: 19
  ident: CR43
  article-title: On the convergence of sequences of linear positive operators in the space of continuous functions of two variables
  publication-title: Dokl. Akad. Nauk SSSR
– volume: 43
  start-page: 213
  issue: 1
  year: 2019
  end-page: 223
  ident: CR44
  article-title: Szász-gamma operators based on Dunkl analogue
  publication-title: Iran. J. Sci. Technol. Trans. A, Sci.
  doi: 10.1007/s40995-017-0433-4
– volume: 40
  start-page: 7749
  year: 2017
  end-page: 7759
  ident: CR26
  article-title: Construction of a new family of Bernstein–Kantorovich operators
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.4559
– volume: 170
  start-page: 197
  year: 1934
  end-page: 217
  ident: CR12
  article-title: Mehrdimensionale differentiation von funktionen mehrerer reeller Veränderlichen
  publication-title: J. Reine Angew. Math.
– ident: CR41
– volume: 114
  year: 2020
  ident: CR38
  article-title: Approximation of functions by a new class of generalized Bernstein–Schurer operators
  publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.
  doi: 10.1007/s13398-020-00903-6
– volume: 42
  start-page: 6580
  year: 2019
  end-page: 6587
  ident: CR20
  article-title: Kantorovich-type generalization of parametric Baskakov operators
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.5762
– volume: 2018
  year: 2018
  ident: 3125_CR15
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-018-1688-9
– volume: 2016
  year: 2016
  ident: 3125_CR1
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-016-1045-9
– volume: 42
  start-page: 6580
  year: 2019
  ident: 3125_CR20
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.5762
– volume: 48
  start-page: 492
  issue: 5
  year: 2019
  ident: 3125_CR29
  publication-title: Int. J. Gen. Syst.
  doi: 10.1080/03081079.2019.1608985
– start-page: 51
  volume-title: Colloq. Math. Soc. János Bolyai
  year: 1990
  ident: 3125_CR9
– volume: 37
  start-page: 137
  issue: 4
  year: 2019
  ident: 3125_CR45
  publication-title: Bol. Soc. Parana. Mat.
  doi: 10.5269/bspm.v37i4.35852
– volume: 14
  start-page: 15
  year: 2007
  ident: 3125_CR39
  publication-title: An. Univ. Oradea, Fasc. Mat.
– ident: 3125_CR41
– volume: 114
  year: 2020
  ident: 3125_CR32
  publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.
  doi: 10.1007/s13398-020-00802-w
– ident: 3125_CR11
– volume: 73
  year: 2018
  ident: 3125_CR3
  publication-title: Results Math.
  doi: 10.1007/s00025-018-0838-1
– volume: 33
  start-page: 4549
  issue: 14
  year: 2019
  ident: 3125_CR30
  publication-title: Filomat
  doi: 10.2298/FIL1914549M
– volume: 2019
  year: 2019
  ident: 3125_CR36
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-019-2055-1
– volume: 2018
  year: 2018
  ident: 3125_CR40
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-018-1909-2
– volume: 11
  issue: 3
  year: 2019
  ident: 3125_CR42
  publication-title: Symmetry
  doi: 10.3390/sym11030316
– year: 2020
  ident: 3125_CR27
  publication-title: Iran. J. Sci. Technol. Trans. A, Sci.
  doi: 10.1007/s40995-020-01024-w
– volume: 34
  start-page: 53
  year: 1986
  ident: 3125_CR8
  publication-title: Bull. Aust. Math. Soc.
  doi: 10.1017/S0004972700004494
– volume: 228
  start-page: 162
  year: 2014
  ident: 3125_CR14
  publication-title: Appl. Math. Comput.
  doi: 10.1016/j.amc.2013.11.095
– volume: 170
  start-page: 197
  year: 1934
  ident: 3125_CR12
  publication-title: J. Reine Angew. Math.
  doi: 10.1515/crll.1934.170.197
– volume-title: Constructive Approximation
  year: 1993
  ident: 3125_CR18
  doi: 10.1007/978-3-662-02888-9
– volume: 4
  start-page: 85
  year: 1966
  ident: 3125_CR19
  publication-title: An. Univ. Timişoara Ser. Şti. Mat.-Fiz.
– volume: 43
  start-page: 213
  issue: 1
  year: 2019
  ident: 3125_CR44
  publication-title: Iran. J. Sci. Technol. Trans. A, Sci.
  doi: 10.1007/s40995-017-0433-4
– volume: 2018
  year: 2018
  ident: 3125_CR16
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-018-1653-7
– volume: 219
  start-page: 9821
  year: 2013
  ident: 3125_CR10
  publication-title: Appl. Math. Comput.
  doi: 10.1016/j.amc.2013.03.115
– year: 2020
  ident: 3125_CR35
  publication-title: Iran. J. Sci. Technol. Trans. A, Sci.
  doi: 10.1007/s40995-020-01018-8
– volume: 36
  start-page: 1178
  issue: 9
  year: 2015
  ident: 3125_CR34
  publication-title: Numer. Funct. Anal. Optim.
  doi: 10.1080/01630563.2015.1056914
– volume: 2018
  year: 2018
  ident: 3125_CR25
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-018-1693-z
– volume: 113
  start-page: 1955
  issue: 3
  year: 2019
  ident: 3125_CR28
  publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.
  doi: 10.1007/s13398-018-0591-z
– volume: 42
  start-page: 655
  year: 2018
  ident: 3125_CR2
  publication-title: Iran. J. Sci. Technol. Trans. A, Sci.
  doi: 10.1007/s40995-016-0045-4
– volume: 33
  start-page: 3473
  issue: 11
  year: 2019
  ident: 3125_CR37
  publication-title: Filomat
  doi: 10.2298/FIL1911473O
– volume: 44
  start-page: 1111
  year: 2020
  ident: 3125_CR23
  publication-title: Iran. J. Sci. Technol. Trans. A, Sci.
  doi: 10.1007/s40995-020-00914-3
– volume: 40
  start-page: 7749
  year: 2017
  ident: 3125_CR26
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.4559
– volume: 4
  start-page: 95
  year: 1988
  ident: 3125_CR7
  publication-title: Approx. Theory Appl.
– volume: 450
  start-page: 244
  year: 2017
  ident: 3125_CR17
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2016.12.075
– volume: 114
  year: 2020
  ident: 3125_CR38
  publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.
  doi: 10.1007/s13398-020-00903-6
– volume: 12
  start-page: 1453
  year: 2018
  ident: 3125_CR4
  publication-title: Complex Anal. Oper. Theory
  doi: 10.1007/s11785-016-0633-5
– volume: 73
  issue: 1
  year: 2018
  ident: 3125_CR22
  publication-title: Results Math.
  doi: 10.1007/s00025-018-0773-1
– volume: 22
  start-page: 73
  year: 2013
  ident: 3125_CR24
  publication-title: Creative Math. Inform.
  doi: 10.37193/CMI.2013.01.09
– volume: 2020
  year: 2020
  ident: 3125_CR31
  publication-title: Adv. Differ. Equ.
  doi: 10.1186/s13662-020-02925-1
– volume: 24
  start-page: 119
  year: 2019
  ident: 3125_CR6
  publication-title: Math. Commun.
– volume: 65
  start-page: 45
  year: 1962
  ident: 3125_CR13
  publication-title: Jahresber. Dtsch. Math.-Ver.
– volume-title: Approximation Theory: Moduli of Continuity and Global Smoothness Preservation
  year: 2000
  ident: 3125_CR5
  doi: 10.1007/978-1-4612-1360-4
– volume: 73
  year: 2018
  ident: 3125_CR21
  publication-title: Results Math.
  doi: 10.1007/s00025-018-0789-6
– volume: 11
  start-page: 85
  issue: 1
  year: 2017
  ident: 3125_CR33
  publication-title: Complex Anal. Oper. Theory
  doi: 10.1007/s11785-016-0572-1
– volume: 115
  start-page: 17
  year: 1957
  ident: 3125_CR43
  publication-title: Dokl. Akad. Nauk SSSR
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Snippet We construct the bivariate form of Bernstein–Schurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the...
We construct the bivariate form of Bernstein–Schurer operators based on parameter α. We establish the Voronovskaja-type theorem and give an estimate of the...
Abstract We construct the bivariate form of Bernstein–Schurer operators based on parameter α. We establish the Voronovskaja-type theorem and give an estimate...
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SubjectTerms Analysis
Applications
Approximation
Bivariate analysis
Bivariate α-Bernstein–Schurer operators
Boolean algebra
Bögel differentiable function
Difference and Functional Equations
Functional Analysis
GBS operators
Mathematical analysis
Mathematics
Mathematics and Statistics
Methods
Modulus of continuity
Operators
Ordinary Differential Equations
Partial Differential Equations
Smoothness
Topics in Special Functions and q-Special Functions: Theory
α-Bernstein operators
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Title Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators
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