幾類廣義平衡問題的不動點迭代法.pdf

1、并證明了由此迭代算法生成的序列的強收斂性第三章研究了一個新的迭代算法用于尋求兩個帶擾動映像的廣義混合平衡問題和有限嚴格偽壓縮映像族公共不動點閻題的公共解，并證明了算法的強收斂性利用此定理，得到了許多新的，有意義的結論第四章研究了一個新的迭代算法用于尋求兩個帶擾動映像的廣義平衡問題和無限非擴張映像族公共不動點問題的公共解，并且證明了由此算法生成的序列的強收斂性第五章研究了一個新的迭代算法用于尋求可數(shù)無窮：i垂強單調(diào)映像組成的兩個平衡問題和

2、無限非擴張映像族的公共不動點問題的公共解證明了一些強收斂性定理第六章研究了一個松弛外梯度方法的修正形式用于尋求帶擾動映像的廣義混合平衡問題，廣義非線性混合復合型平衡的一般系統(tǒng)以及嚴格偽壓縮映像不動點問題的公共解，并且得到了一個強收斂性定理利用此定理，建立了一些在不動點問題，變分不等式，混合平衡問題以及廣義非線性混合復合型平衡的系統(tǒng)方面的強收斂性結果關鍵詞：非擴張映像；嚴格偽壓縮映象；逆一強單調(diào)映像；不動點；變分不等式；平衡問題；帶擾動映

3、像的廣義混合平衡問題；廣義非線性混合復合型平衡的系統(tǒng)；強收斂性；上海師范大學博士學位論文4IlIlllllII刪IIIllllIIIllI|IIllIIⅢmIY2096706AbstmctFixedPointIterationMethodsforSeveralClassesofGeneralizedEquilibriumPToblemsAbstractInrecentyears，variationalinequalitytheoryha

4、sbeenbecomeveryeffectiveandpowerfultoolsforstudyingawideclassofnonlinearproblemsarisinginmanydiversefieldsofpuremathematicsandappliedsciencesAsageneralizationofvariationalinequalityproblemtheequilibriumproblembecomesoneo

5、fthemostimportantandmostusefulproblemsatpresentIthadahugeimpactonmanybranchesofpuremathematicsandappliedmathemaAicsAtthesametime，theequilibriumproblemhasbeenextensivelyandintensivelyappliedtomechanics，physics，moderncontr

6、ol，nonlinearprogramming，economicalequilibriumandmanyotherareasItiswellknownthatoneofthemostimportantanddifficultproblemsinvariationalinequalitytheoryistodevelopeffectiveandimplementableiterativealgorithmsforcomputingappr

7、oximatesolutionsandtoanalysetheconvergenceofthealgorithnlsTherefore，amongthetasksofstudyingtheequilibriumproblem，oneimportanttaskistheconstructionofiterativemethodsforthecommonsolutionofequilibriumproblems，variationaline

8、qualityproblemsandfixedpointproblemsTheaimofthisthesisistoinvestigateiterativemethodsforthecommonsolutionoftheseproblemswithapplicationsinconcreteexampleaThethesisconsistsofsixchaptersInChapter1，wefirststatetheresearchba

9、ckgroundandgivethesummaryoftheworkinthispaperInChapter2，wearedevotedtoinvestigatinganewiterativealgorithmforfindingacoinInonsolutionofageneralizedequilibriumproblemwithperturbedmappingandthefixedpointproblemofastrictpseu

10、docontractivemappingThenthestrongconvergenceofthesequencegeneratedbythisiterativealgorithmisprovenInChapter3，wearedevotedtoinvestigatinganewiterativeschemeforfindingacoIIlinonsolutionoftwogeneralizedmixedequilibriumprobl

11、emswithperturbedmappingsandacommonfixedpointproblemofafinitefamilyofstrictpseudocontractivemappingsStrongconvergencetheoremisestablishedintheframeworkofHilbertspacesApplyingthisresult，骶alsogetsomenewandinterestingresults