廣義Heronian均值函數(shù)與Hamy對稱函數(shù)的研究.pdf

1、內(nèi)蒙古民族大學(xué)碩士學(xué)位論文廣義Heronian均值函數(shù)與Hamy對稱函數(shù)的研究姓名：張濤申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：寶音特古斯20100401StudiesonGeneralizedHeronianMeansandHamySymmetricFuctionsAbstractInequalityexistsinalmosteveryaspectsofmathematicalsciencesForexample，Analysis

2、Inequality，MatrixInequalityProbabilityAndStatisticsInequality，SpecialFunctionInequality，VariationalInequality，GeometricInequality，F(xiàn)nctionalAnalysisInequality，IntegralInequality，DifferentialInequality，AlgebraicInequalitie

3、s，NumberTheoryInequalityMathematicalInequalitiesinPureandAppliedMathematics(example：MultiDimensionalStatistics，ProbabilityTheory，Analysis，OptimizationTheory，InformationTheory，ApproximationTheory，GraphTheory)playsakeyrole

4、Therefore，asthemostbasicinequalityofinequalitytheorypinequalityofmeansisveryimportantTheSchurconvexityofHamysymmetricfunctionsisanimportanttooltOestablishandanalysisinequalityTherefore，twa：lassesofgeneralizedHamysymmetri

5、cfunctionsarediscussedinthispaperThisarticleisdividedintothreechapters：InChapterIstatesbrieflythecourseofdevelopment，researchingstatusquoandtheprojectworkofthisthesisInChapter2，themonotonicityandtheconvexityofthefollowin

6、ggeneraliedf，P一?？?，6，：彳[蘭蘭摯]彤，r≥。p≠。屆W=柵勘=0andthefollowingnewinequalityareestablished：x’(27—2)x；y；y’≤(≥)(xy)7≤(≥)吾(工7(2，一2)x；y；y7)comparedHp。(皿6)andthepowermeansMq(a，b)bywhichwherew，=∥=Moreoveranecessaryandsufficientcondi