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Journal of Zhejiang University (Science Edition)  2023, Vol. 50 Issue (5): 533-538    DOI: 10.3785/j.issn.1008-9497.2023.05.003
Mathematics and Computer Science     
Approximation properties of q-type Lupas-Kantorovich operators
Tao WANG1(),Yan LI2
1.School of Mathematics and Statistics,Shandong University of Technology,Zibo 255049,Shandong Province,China
2.Zichuan Middle School,Zibo 255100,Shandong Province,China
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Abstract  

We construct a q-type Lupas-Kantorovich operators based on the q-type integer and q-type calculus, investigate the rate of convergence of q-type Lupas-Kantorovich operators by modulus continuity as well as the properties of statistical convergence and weighted statistical convergence of the operators.



Key wordsq-type Lupas-Kantorovich operators      q-type calculus      statistical convergence      weighted statistical convergence     
Received: 16 September 2022      Published: 16 September 2023
CLC:  O 174.41  
Cite this article:

Tao WANG,Yan LI. Approximation properties of q-type Lupas-Kantorovich operators. Journal of Zhejiang University (Science Edition), 2023, 50(5): 533-538.

URL:

https://www.zjujournals.com/sci/EN/Y2023/V50/I5/533


q-型Lupas-Kantorovich算子的逼近性质

利用q-型微积分构造了一种基于q-型整数的q-型Lupas-Kantorovich算子,利用连续模研究了q-型Lupas-Kantorovich算子的逼近速度、q-型Lupas-Kantorovich算子加权逼近性质和加权统计收敛性质。


关键词: q-型Lupas-Kantorovich算子,  q-型微积分,  统计收敛,  加权统计收敛 
[1]   LUPAS A. A q-analogue of Bernstein operator[C]// Seminar on Numerical an Statistical Calculus. Cluj-Napoca: University of Cluj-Napoca, 1987, 9:85-92.
[2]   PHILLIPS G M. Bernstein polynomials based on q-integers[J]. Annals of Numerical Mathematics, 1996, 4(1): 511-518. DOI:10.1007/0-387-21682-07
doi: 10.1007/0-387-21682-07
[3]   GUPTA V, WANG H. The rate of convergence of q-Durrmeyer operators for 0 < q < 1 [J]. Mathematical Methods in the Applied Sciences, 2008, 31(16): 1946-1955. DOI:10.1002/mma.1012
doi: 10.1002/mma.1012
[4]   AGRAWAL P N, KUMAR A S. Approximation by q-Baskakov Durrmeyer type operators[J]. Rendiconti Del Circolo Matematico Di Parlerma, 2013, 63(1): 73-89. DOI:10.1007/s12215-013-0142-6
doi: 10.1007/s12215-013-0142-6
[5]   SINGH K K, GAIROlA A R, DEEPMALA. Approximation theorem for q-analouge of a linear positive operators by a Lupas[J]. International Journal of Analysis and Application, 2016, 12(1): 30-37. DOI:j.issn.2291-8639
doi: j.issn.2291-8639
[6]   ORKCU M, DOGRU O. q-Szasz-Mirakyan-Kantorovich type operators preserving some test functions[J]. Applied Mathematics Letters, 2011, 24(4): 1588-1593. DOI:10.1016/j.aml.2011.04.001
doi: 10.1016/j.aml.2011.04.001
[7]   DOGRU O, KANAT K. On statistical approximation properties of the Kantorovich type Lupas operators [J]. Mathematical and Computer Modelling, 2012, 55: 1610-1621. DOI:10.1016/j.mcm.2011.10.059
doi: 10.1016/j.mcm.2011.10.059
[8]   MISHRA V N, KHATRI K, MISHRA L N. Statistical approximation by Kantorovich-type discreate q-Beta operators[J]. Advances in Difference Equations, 2013, 345: 1-15. DOI:10.1186/1687-1847-2013-345
doi: 10.1186/1687-1847-2013-345
[9]   GUPTA V, RASSIAS T M, YADAV R. Approximation by Lupas-Beta integral operators[J]. Applied Mathematics and Computation, 2014, 236(3): 19-26. DOI:10.1016/j.amc.2014.03.033
doi: 10.1016/j.amc.2014.03.033
[10]   DUMAN O, ORHAN C. Statistical approximation by positive linear operators[J]. Studia Mathematica, 2006,161(2): 187-197. DOI:10.4064/sm-161-2-6
doi: 10.4064/sm-161-2-6
[11]   MURSALEEN M, ALABIED A A H, ANSARI K J. On approximation properties of Baskakov-Schurer-Szasz-Stancu operators based on q-integers[J]. Filomat, 2018, 32(4): 1359-1378. DOI:10.1016/j.aej.2021.04.038
doi: 10.1016/j.aej.2021.04.038
[12]   GADJIEV A D, ORHAN C. Some approximation theorems via statistical convergence[J]. Rock Mountain Journal of Mathematics, 2002, 32(1): 129-138. doi:10.1216/rmjm/1030539612
doi: 10.1216/rmjm/1030539612
[13]   KAC V, CHEUNG P. Quantum Calculus[M]. New York: Springer-Verlag, 2002: 1-79. doi:10.1007/978-1-4613-0071-7_26
doi: 10.1007/978-1-4613-0071-7_26
[14]   ARAL A, GUPTA V, AGARWAL R. Applications of q-Calculus in Operator Theory[M]. New York: Springer-Verlag, 2013: 1-72. DOI:10. 1007/978-1-4614-6946-9
doi: 10. 1007/978-1-4614-6946-9
[15]   ANASTASSIOU G A, DUMAN O. Towards Intelligent Modeling Statistical Approximation Theory[M]. New York: Springer-Verlag, 2011: 1-37. DOI:10.1007/978-3-642-19826-7
doi: 10.1007/978-3-642-19826-7
[16]   LUPAS A. The approximation by some positive linear operators[C]// Proceedings of the International Dortmund Meeting on Approximation Theory. Berlin: Akademie Verlag, 1995, 86: 201-229. doi:10.1006/jath.1996.0057
doi: 10.1006/jath.1996.0057
[17]   AGRATINI O. On the rate of convergence of a positive approximation process[J]. Nihonkai Mathematical Journal, 2000, 11(1): 47-56. doi:10.18514/mmn.2001.31
doi: 10.18514/mmn.2001.31
[18]   王涛. Lupas算子对局部有界函数的点态逼近估计[J]. 山东大学学报(理学版), 2020, 55(2): 9-15. DOI:10. 6040/j.issn.1671-9352.0.2019.067
WANG T. Pointwise approximation of Lupas operators to locallly bounded functions[J]. Journal of Shandong University(Science Edition), 2020, 55(2): 9-15. DOI:10.6040/j.issn.1671-9352.0. 2019.067
doi: 10.6040/j.issn.1671-9352.0. 2019.067
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