On the Rate of Convergence by Generalized Baskakov Operators
We firstly construct generalized Baskakov operators Vn,α,q(f;x) and their truncated sum Bn,α,q(f;γn,x). Secondly, we study the pointwise convergence and the uniform convergence of the operators Vn,α,q(f;x), respectively, and estimate that the rate of convergence by the operators Vn,α,q(f;x) is 1/nq/...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/564854 |
| Summary: | We firstly construct generalized Baskakov operators Vn,α,q(f;x) and their truncated sum Bn,α,q(f;γn,x). Secondly, we study the pointwise convergence and the uniform convergence of the operators Vn,α,q(f;x), respectively, and estimate that the rate of convergence by the operators Vn,α,q(f;x) is 1/nq/2. Finally, we study the convergence by the truncated operators Bn,α,q(f;γn,x) and state that the finite truncated sum Bn,α,q(f;γn,x) can replace the operators Vn,α,q(f;x) in the computational point of view provided that limn→∞nγn=∞. |
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| ISSN: | 1687-9120 1687-9139 |