C_-代数及几类空间上泛函方程的稳定性

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6、K.'c:Hyers-Ulam½5;C∗-ê;N;gN;ngN;n<âm;CÄn<âm.iHÆa¬ÆØ©AbstractThestabilityproblemoffunctionalequationsoriginatedfromaquestionofUlamconcerningthestabilityofgrouphomomorphismsin1940:Giveagroup(G1,∗)andametricgroup(G2,·,d)withthemetricd(·,·).Give>0,doesthe

7、reexistsaδ>0suchthatiff:G1→G2satisfiesd(f(x∗y),f(x)·f(y))<δforallx,y∈G1,thenisthereahomomorphismg:G1→G2withd(f(x),g(x))<εforallx∈G1?In1941,D.H.HyerssolvedthestabilityproblemofadditivemappingonBanachspaces.Inthefollowingdecades,manymathematicianshavestudiedthe

8、stabilityofdifferentkindsoffunctionalequationssuchasexponentialequation,quadraticfunctionalequation,cubicfunctionalequation,generalizedadditiveequationandsoon.In1978,Th.M.RassiassolvedthestabilityproblemoflinearmappinginBanachspace.In1999,Y.LeeandK.Junstudied

9、thestabilityofgeneralizedJensenequation.Thesestabilityresultshaveapplicationsinsomerelatedfieldssuchasrandomanalysis,financialmathematicsandactuarialmathematics.Thisthesisconsistsoftwochapters.Inc