On the rate of convergence by generalized Baskakov operators

Gao, Yi and Wang, W. and Yue, Shigang (2015) On the rate of convergence by generalized Baskakov operators. Advances in Mathematical Physics, 2015 . p. 564854. ISSN 1687-9120

Full content URL: http://www.hindawi.com/journals/amp/2015/564854/

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On the rate of convergence by generalized Baskakov operators
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Abstract

We firstly construct generalized Baskakov operators V n, α, q (f; x) and their truncated sum B n, α, q (f; γ n, x). Secondly, we study the pointwise convergence and the uniform convergence of the operators V n, α, q (f; x), respectively, and estimate that the rate of convergence by the operators V n, α, q (f; x) is 1 / n q / 2. Finally, we study the convergence by the truncated operators B n, α, q (f; γ n, x) and state that the finite truncated sum B n, α, q (f; γ n, x) can replace the operators V n, α, q (f; x) in the computational point of view provided that l i m n → ∞ n γ n = ∞. © 2015 Yi Gao et al.

Additional Information:This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords:convergence, Convergence of numerical methods, Baskarov operators, JCOpen
Subjects:G Mathematical and Computer Sciences > G400 Computer Science
F Physical Sciences > F340 Mathematical & Theoretical Physics
Divisions:College of Science > School of Computer Science
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ID Code:17367
Deposited On:08 May 2015 09:04

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