幾類廣義平衡問題的不動(dòng)點(diǎn)迭代法.pdf

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

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

3、像的廣義混合平衡問題；廣義非線性混合復(fù)合型平衡的系統(tǒng)；強(qiáng)收斂性；上海師范大學(xué)博士學(xué)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