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九五品
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作者G.Hardy、J.E.Littlewood G.Polya 著
出版社世界图书出版公司
出版时间2004-04
版次1
装帧平装
上书时间2024-09-14
商品详情
- 品相描述:九五品
图书标准信息
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作者
G.Hardy、J.E.Littlewood G.Polya 著
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出版社
世界图书出版公司
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出版时间
2004-04
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版次
1
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ISBN
9787506266062
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定价
59.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
324页
- 【内容简介】
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Itisoftenreallydifficulttotracetheoriginofafamiliarinequality.Itisquitelikelytooccurfirstasanauxiliaryproposition,oftenwithoutexplicitstatement,inamemoirongeometryorastronomy;itmayhavebeenrediscovered,manyyearslater,byhalfadozendifferentauthors;andnoaccessiblestatementofitmaybequitecomplete.Wehavealmostalwaysfound,evenwiththemostfamousinequalities,thatwehavealittlenewtoadd.Wehavedoneourbesttobeaccurateandhavegivenallreferenceswecan,butwehaveneverundertakensystematicbibliographicalresearch.Wefollowthecommonpractice,whenaparticularinequalityishabituallyassociatedwithaparticularmathematiciansname;wespeakoftheinequalitiesofSchwarz,HSlder,andJensen,thoughalltheseinequalitiescanbetracedfurtherback;andwedonotenumerateexplicitlyalltheminoradditionswhicharenecessaryforabsolutecompleteness.Wehavereceivedagreatdealofassistancefromfriends.MessrsG.A.Bliss,L.S.Bosanquet,R.Courant,B.Jessen,V.Levin,R.Rado,I.Schur,L.C.Young,andA.Zygmundhaveallhelpeduswithcriticismsororiginalcontributions.DrBosanquet,DrJessen,andProf.Zygmundhavereadthoproofs,andcorrectedmanyinaccuracies.Inparticular,ChapterIIIhasbeenverylargelyrewrittenastheresultofDrJessenssuggestions.Wehopethatthebookmaynowbereasonablyfreefromerror,inspiteofthemassofdetailwhichitcontains.
本书为英文版。
- 【目录】
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CHAPTERⅠINTRODUCTION
1.1Finite,infinite,andintegralinequalities
1.2Notations
1.3Positiveinequalities
1.4Homogeneousinequalities
1.5Theaxiomaticbasisofalgebraicinequalities
1.6Comparablefunctions
1.7Selectionofproofs
1.8Selectionofsubjects
CHAPTERⅡELEMENTARYMEANVALUES
2.1Ordinarymeans
2.2Weightedmeans
2.3Limitingcasesofa
2.4Cauchysinequality
2.5Thetheoremofthearithmeticandgeometricmeans
2.6Otherproofsofthetheoremofthemeans
2.7Holdersinequalityanditsextensions
2.8Holdersinequalityanditsextensionscont
2.9Generalpropertiesofthemeansa
2.10Thesumsra
2.11Minkowskisinequality
2.12AcompaniontoMinkowskisinequality
2.13Illustrationsandapplicationsofthefundamentalinequalities
2.14Inductiveproofsofthefundamentalinequalities
2.15ElementaryinequalitiesconnectedwithTheorem37
2.16ElementaryproofofTheorem3
2.17Tchebyehefsinequality
2.18Muirheadstheorem
2.19ProofofMuirheadstheorem
2.20Analternativetheorem
2.21Furthertheoremsonsymmetricalmeans
2.22Theelementarysymmetricfunctionsofnpositivenumbers
2.23Anoteondefiniteforms
2.24AtheoremconcerningstrictlypositiveformsMiscellaneoustheoremsandexamples
CHAPTERⅢMEANVALUESWITHANARBITRARYFUNCTIONANDTHETHEORYOFCONVEXFUNCTIONS
3.1Definitions
3.2Equivalentmeans
3.3Acharacteristicpropertyofthemeans
3.4Comparability
3.5Convexfunctions
3.6Continuousconvexfunctions
3.7Analternativedefinition
3.8Equalityinthefundamentalinequalities
3.9RestatementsandextensionsofTheorem85
3.10Twicedifferentiableconvexfunctions
3.11Applieationsofthepropertiesoftwicedifferentiableconvexfunctions
3.12Convexfunctionsofseveralvariables
3.13GeneralisationsofHoldersinequality
3.14Sometheoremsconcerningmonotonicfunctions
3.15Sumswithanarbitraryfunction:generalisa.tionsofJensensinequality
3.16GeneralisationsofMinkowskisinequality
3.17Comparisonofsets
3.18Furthergeneralpropertiesofconvexfunctions
3.19Furtherpropertiesofcontinuousconvexfunctions
3.20DiscontinuousconvexfunctionsMiscellaneoustheoremsandexamples
……
CHAPTERⅣVARIOUSAPPLICATIONSOFTHECALCULUS
CHAPTERⅤINFINITESERIES
CHAPTERⅥINTEGRALS
CHAPTERⅦSOMEAPPLICATIONSOFTHECALCULUSOFVARIATIONS
CHARTERⅧSOMETHEOREMSCONCERNINGBILINEARANDMULTILINEARFORMS
CHAPTERⅨHILBERTSINEQUALITYANDITSANALOGUESANDEXTENSIONS
CHAPTERⅩREARRANGEMENTS
APPENDIXⅠOnstrictlypositiveforms
APPENDIXⅡThorinsproofandextensionofTheorem295
APPENDIXⅢOnHilbertsinequality
BIBLIOGRAPHY
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