Baskakov-Kantorovich算子在紧圆盘上的同时逼近性质
Simultaneous Approximation Properties of Complex Baskakov-Kantorovich Operators in Compact Disks
DOI: 10.12677/PM.2018.83033, PDF,    国家自然科学基金支持
作者: 李文霞*, 齐秋兰：河北师范大学数学与信息科学学院，河北 石家庄
关键词: Baskakov-Kantorovich算子；同时逼近；Voronovskaja型结果；Baskakov-Kantorovich Operators； Simultaneous Approximation； Voronovskaja-Type Results
摘要: 本文根据Baskakov-Kantorovich算子在复空间的定义及性质研究Baskakov-Kantorovich算子在复空间的逼近性质，得到了Baskakov-Kantorovich算子在紧圆盘上的同时逼近性质。
Abstract: In this paper, the approximation properties of the Baskakov-Kantorovich operators in the complex space are studied according to the definition and properties of the operator in the complex space. We obtain the simultaneous approximation order for complex Baskakov-Kantorovich operators attached to entire functions or to analytic functions in compact disks.
文章引用：李文霞, 齐秋兰. Baskakov-Kantorovich算子在紧圆盘上的同时逼近性质[J]. 理论数学, 2018, 8(3): 259-264. https://doi.org/10.12677/PM.2018.83033

参考文献

[1] Ditzian, Z. and Totik, V. (1987) Modulus of Smoothness. Springer-Verlag, Berlin/New York. [Google Scholar] [CrossRef] 
[2] Guo, S. and Qi, Q. (2003) Strong Converse Inequalities for Baskakov Opera-tors. Journal of Approximation Theory, 124, 219-231. [Google Scholar] [CrossRef] 
[3] Ispir, N. (2007) Rate of Convergence of Generalized Rational Type Baskakov Operators. Mathematical and Computer Modelling, 46, 625-631. [Google Scholar] [CrossRef] 
[4] Govil, N.K. and Gupta, V. (2008) Convergence Rate for Generalized Baskakov Type Operators. Nonlinear Analysis, 69, 3795-3801. [Google Scholar] [CrossRef] 
[5] Gal, S.G. (2009) Ap-proximation by Complex Bernstein and Convolution-Type Operators. World Scientific Publ Co., Singapore, Hong Kong, London, New Jersey. [Google Scholar] [CrossRef] 
[6] Mahmudov, N.I. and Kara, M. (2013) Approximation Theorems for Complex Szász-Kantorovich Operators. Journal of Computational Analysis and Applications, 15, 32-38.
[7] Gal, S.G. and Opris, B.D. (2015) Approximation with an Arbitrary Order by Modified Baskakov-Type Operators. Applied Mathematics and Computation, 265, 329-332. [Google Scholar] [CrossRef] 
[8] Gal, S.G. and Opris, B.D. (2016) Approximation of Analytic Functions with an Arbitrary Order by Generalized Baskakov-Faber Operators in Compact Sets. Complex Analysis and Operator Theory, 10, 369-377. [Google Scholar] [CrossRef] 
[9] Gal, S.G., Mahmudov, N.I. and Opris, B.D. (2016) Approximation with an Arbitrary Order by Szász-Kantorovich and Baskakov Complex Operators in Compact Disks. Azerbaijan Journal of Mathematics, 6, 3-12.
[10] Gal, S.G. and Gupta, V. (2014) Approximation by Complex Szasz-Durrmeyer Operators in Compact Disks. Acta Mathe-matica Scientia, 34B, 1157-1165. [Google Scholar] [CrossRef] 
[11] 钟玉泉. 复变函数论[M]. 第三版. 北京: 高等教育出版社, 2004.
[12] 李文霞, 齐秋兰. Baskakov-Kantorovich型算子在紧圆盘上的逼近性质[J]. 数学物理学报, 2018, 38A(4).

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