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Article: Sharp Cusa and Becker-Stark inequalities
| Title | Sharp Cusa and Becker-Stark inequalities | ||||
|---|---|---|---|---|---|
| Authors | |||||
| Keywords | Inequalities Trigonometric functions | ||||
| Issue Date | 2011 | ||||
| Publisher | SpringerOpen. The Journal's web site is located at http://www.journalofinequalitiesandapplications.com | ||||
| Citation | Journal of Inequalities and Applications, 2011, v. 2011, article no. 136 How to Cite? | ||||
| Abstract | We determine the best possible constants θ,ϑ,α and β such that the inequalities ((2+cosx)/3)^θ < sinx/x < ((2+cosx)/3)^ϑ and ((π^2)/(π^2-4×^2))^α < tan×/× < ((π^2)/(π^2-4×^2))^β are valid for 0 < × < π/2. Our results sharpen inequalities presented by Cusa, Becker and Stark. | ||||
| Persistent Identifier | http://hdl.handle.net/10722/144549 | ||||
| ISSN | 2010 Impact Factor: 0.879 2023 SCImago Journal Rankings: 0.448 | ||||
| ISI Accession Number ID |
Funding Information: Research is supported in part by the Research Grants Council of the Hong Kong SAR, Project No. HKU7016/07P. |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Chen, CP | en_US |
| dc.contributor.author | Cheung, WS | en_US |
| dc.date.accessioned | 2012-02-03T06:13:18Z | - |
| dc.date.available | 2012-02-03T06:13:18Z | - |
| dc.date.issued | 2011 | en_US |
| dc.identifier.citation | Journal of Inequalities and Applications, 2011, v. 2011, article no. 136 | en_US |
| dc.identifier.issn | 1025-5834 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/144549 | - |
| dc.description.abstract | We determine the best possible constants θ,ϑ,α and β such that the inequalities ((2+cosx)/3)^θ < sinx/x < ((2+cosx)/3)^ϑ and ((π^2)/(π^2-4×^2))^α < tan×/× < ((π^2)/(π^2-4×^2))^β are valid for 0 < × < π/2. Our results sharpen inequalities presented by Cusa, Becker and Stark. | - |
| dc.language | eng | en_US |
| dc.publisher | SpringerOpen. The Journal's web site is located at http://www.journalofinequalitiesandapplications.com | - |
| dc.relation.ispartof | Journal of Inequalities and Applications | en_US |
| dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
| dc.subject | Inequalities | - |
| dc.subject | Trigonometric functions | - |
| dc.title | Sharp Cusa and Becker-Stark inequalities | en_US |
| dc.type | Article | en_US |
| dc.identifier.email | Chen, CP: chenchaoping@sohu.com | en_US |
| dc.identifier.email | Cheung, WS: wscheung@hkucc.hku.hk | - |
| dc.identifier.authority | Cheung, WS=rp00678 | en_US |
| dc.description.nature | published_or_final_version | - |
| dc.identifier.doi | 10.1186/1029-242X-2011-136 | - |
| dc.identifier.scopus | eid_2-s2.0-84868246301 | - |
| dc.identifier.hkuros | 198523 | en_US |
| dc.identifier.volume | 2011, article no. 136 | en_US |
| dc.identifier.isi | WOS:000301733000001 | - |
| dc.publisher.place | Germany | - |
| dc.identifier.issnl | 1025-5834 | - |