非線性算子的迭代算法.pdf

1、天津工業(yè)大學(xué)碩士學(xué)位論文非線性算子的迭代算法姓名：賀慧敏申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：陳汝棟20071201AbstractThefixedpointtheoryofnonlinearoperatorsisanconstituentimportantpartofnonlinearfunctionalanalysis，especially，theproblemofapproximatingtosolutionsofnonlin

2、earoperatorequationsbecomesthetopicthatpeoplestudyintherecentlyyearsSpeciallynonlinearoperatorsemigroupscommonfixedpointtheoryisalsoanconstituentimportantpartofnonlinearfunctionalanal—ysisForaratherlongtime，manyauthorsha

3、vebeenusingHaperniterativemethodsandmodifiedManniterativemethodsforcomputingsolutionstonon1inearoperatorequationsorthefixedpointsofnonlinearoperatorsgroupsInthispaper，wehavemainlyusedseveraldifferentmethodstodoresearchon

4、nonexpansivemappingssemigroups，asymptoticallypseudocontractivemappingssemigroups，afinitefamilyhemicontractivemappings，pseudocontractivemappingsandnonexpansivemappings，andwehavegainedsomestronglyconvergencetheoriesResults

5、presentedinthispaperimprove，extendandunifymanyauthors’Srecentresults。ThispaperincludesfivechaptersNowwewilldescribethembrieflyonebyoneChapter1statesthatpresentsituationofiterationalgorithmsforsolutionsofnonlinearoperator

6、equationsinHilbertspacesandBanachspaces，andwealsogiveadevelopmentstageofthisworkChapter2mainlyconcernsaboutiterativeapproximationproblemsfornonexpansivemappingssemigroupsChapter3mainlydiscussesaboutiterativeapproximation

7、problemsforasymptoticallypseudocontractivemappingssemigroupsChapter4paysattentiontoiterativeapproximationproblemsforafinitefamilyhemicontractivemappingsThelastChaptermainlyconsidersapproximatingfixedpointsofpseudocontrac