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简介：LetEbeauniformlysmoothBanachspace,KbeanonemptyclosedconvexsubsetofE,andsuppose:T:K→Kisacontinuousφ-stronglypseudocontractiveoperatorwithaboundedrange.Usinganewanalyticalmethod,undergeneralcases,theIshikawaiterativeprocess{xn}convergesstronglytotheuniquefixedpointx*oftheoperatorTwereproved.Thepapergeneralizesandextendsalotofrecentcorrespondingresults.

简介：TheexistenceofsolutionsforsystemsofnonlinearimpulsiveVolterraintegralequationsontheinfiniteintervalR+withaninfinitenumberofmomentsofimpulseeffectinBanachspacesisstudied.Someexistencetheoremsofextremalsolutionsareobtained,whichextendtherelatedresultsforthisclassofequationsonafiniteintervalwithafinitenumberofmomentsofimpulseeffect.Theresultsaredemonstratedbymeansofanexampleofaninfinitesystemsforimpulsiveintegralequations.

简介：ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１］ｔｈｅｅｘｉｓｔｅｎｃｅａｎｄｉｔｅｒａｔｉｖｅａｐｐｒｏｘｉｍａｔｉｏｎｏｆｍｉｎｉｍａｘｑｕａｓｉ＿ｓｏｌｕｔｉｏｎｓｆｏｒｔｈｅｆｏｌｌｏｗｉｎｇＩＶＰ（＊）ｏｆｆｉｒｓｔｏｒｄｅｒｉｍｐｕｌｓｉｖｅｄｉｆｆｅ...

简介：AnewclassofalmostasymptoticallynonexpansivetypemappingsinBanachspacesisintroduced,whichincludesanumberofknownclassesofnonlinearLipschitzianmappingsandnon-LipschitzianmappingsinBanachspacesasspecialcases;forexample,theknownclassesofnonexpansivemappings,asymptoticallynonexpansivemappingsandasymptoticallynonexpansivetypemappings.TheconvergenceproblemofmodifiedIshikawaiterativesequenceswitherrorsforapproximatingfixedpointsofalmostasymptoticallynonexpansivetypemappingsisconsidered.NotonlyS.S.Chang'sinequalitybutalsoH.K.Xu'soneforthenormsofBanachspacesareappliedtomaketheerrorestimatebetweentheexactfixedpointandtheapproximateone.Moreover,ZhangShi-sheng'smethod(AppliedMathematicsandMechanics(EnglishEdition),2001,22(1):25-34)formakingtheconvergenceanalysisofmodifiedIshikawaiterativesequenceswitherrorsisextendedtothecaseofalmostasymptoticallynonexpansivetypemappings.ThenewconvergencecriteriaofmodifiedIshikawaiterativesequenceswitherrorsforfindingfixedpointsofalmostasymptoticallynonexpansivetypemappingsinuniformlyconvexBanachspacesarepresented.Also,thenewconvergencecriteriaofmodifiedManniterativesequenceswitherrorsforthisclassofmappingsareimmediatelyobtainedfromthesecriteria.Theaboveresultsunify,improveandgeneralizeZhangShi-sheng'sonesonapproximatingfixedpointsofasymptoticallynonexpansivetypemappingsbythemodifiedIshikawaandManniterativesequenceswitherrors.

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简介：Anewbilevelgeneralizedmixedequilibriumproblem(BGMEP)involvinggeneralizedmixedvariational-likeinequalityproblems(GMVLIPs)isintroducedandstudiedinthereflexiveBanachspaces.First,anauxiliarygeneralizedmixedequilibriumproblem(AGMEP)isintroducedtocomputetheapproximatesolutionsoftheBGMEPinvolvingtheGMVLIPs.Byusingaminimaxinequality,theexistenceandtheuniquenessofsolutionsoftheAGMEPareprovedundermildconditionswithoutanycoerciveassumptions.Byusinganauxiliaryprincipletechnique,thenewiterativealgorithmsareproposedandanalyzed,withwhichtheapproximatesolutionsoftheBGMEParecomputed.Thestrongconvergenceoftheiterativesequencegeneratedbythealgorithmsisshownundermildconditionswithoutanycoerciveassumptions.Thesenewresultscangeneralizesomerecentresultsinthisfield.