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Article: Sharp Cusa and Becker-Stark inequalities

TitleSharp Cusa and Becker-Stark inequalities
Authors
KeywordsInequalities
Trigonometric functions
Issue Date2011
PublisherSpringerOpen. 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?
AbstractWe 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 Identifierhttp://hdl.handle.net/10722/144549
ISSN
2010 Impact Factor: 0.879
2015 SCImago Journal Rankings: 0.478
ISI Accession Number ID
Funding AgencyGrant Number
Research Grants Council of the Hong Kong SARHKU7016/07P
Funding Information:

Research is supported in part by the Research Grants Council of the Hong Kong SAR, Project No. HKU7016/07P.

 

DC FieldValueLanguage
dc.contributor.authorChen, CPen_US
dc.contributor.authorCheung, WSen_US
dc.date.accessioned2012-02-03T06:13:18Z-
dc.date.available2012-02-03T06:13:18Z-
dc.date.issued2011en_US
dc.identifier.citationJournal of Inequalities and Applications, 2011, v. 2011, article no. 136en_US
dc.identifier.issn1025-5834-
dc.identifier.urihttp://hdl.handle.net/10722/144549-
dc.description.abstractWe 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.languageengen_US
dc.publisherSpringerOpen. The Journal's web site is located at http://www.journalofinequalitiesandapplications.com-
dc.relation.ispartofJournal of Inequalities and Applicationsen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectInequalities-
dc.subjectTrigonometric functions-
dc.titleSharp Cusa and Becker-Stark inequalitiesen_US
dc.typeArticleen_US
dc.identifier.emailChen, CP: chenchaoping@sohu.comen_US
dc.identifier.emailCheung, WS: wscheung@hkucc.hku.hk-
dc.identifier.authorityCheung, WS=rp00678en_US
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1186/1029-242X-2011-136-
dc.identifier.scopuseid_2-s2.0-84868246301-
dc.identifier.hkuros198523en_US
dc.identifier.volume2011, article no. 136en_US
dc.identifier.isiWOS:000301733000001-
dc.publisher.placeGermany-

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