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: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2015-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/564854 |
| id |
doaj-667280e70e234bcca478ca05c019d5b5 |
|---|---|
| record_format |
Article |
| spelling |
doaj-667280e70e234bcca478ca05c019d5b52021-07-02T08:35:34ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/564854564854On the Rate of Convergence by Generalized Baskakov OperatorsYi Gao0Wenshuai Wang1Shigang Yue2School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan, Ningxia 750021, ChinaSchool of Mathematics and Computer Science, Ningxia University, Yinchuan, Ningxia 750021, ChinaSchool of Computer Science, University of Lincoln, Lincoln LN6 7TS, UKWe 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=∞.http://dx.doi.org/10.1155/2015/564854 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yi Gao Wenshuai Wang Shigang Yue |
| spellingShingle |
Yi Gao Wenshuai Wang Shigang Yue On the Rate of Convergence by Generalized Baskakov Operators Advances in Mathematical Physics |
| author_facet |
Yi Gao Wenshuai Wang Shigang Yue |
| author_sort |
Yi Gao |
| title |
On the Rate of Convergence by Generalized Baskakov Operators |
| title_short |
On the Rate of Convergence by Generalized Baskakov Operators |
| title_full |
On the Rate of Convergence by Generalized Baskakov Operators |
| title_fullStr |
On the Rate of Convergence by Generalized Baskakov Operators |
| title_full_unstemmed |
On the Rate of Convergence by Generalized Baskakov Operators |
| title_sort |
on the rate of convergence by generalized baskakov operators |
| publisher |
Hindawi Limited |
| series |
Advances in Mathematical Physics |
| issn |
1687-9120 1687-9139 |
| publishDate |
2015-01-01 |
| description |
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=∞. |
| url |
http://dx.doi.org/10.1155/2015/564854 |
| work_keys_str_mv |
AT yigao ontherateofconvergencebygeneralizedbaskakovoperators AT wenshuaiwang ontherateofconvergencebygeneralizedbaskakovoperators AT shigangyue ontherateofconvergencebygeneralizedbaskakovoperators |
| _version_ |
1721334511410610176 |