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1、..第1卷第1期應用泛函分析學報11,1999年6月CLFCLLC19T99YSSUPPTSmoothPointsandStrong(very)Smooth一rPointsofMusielakOliczSPaceswithorliCzNormn一ulU。ngZWANGTigfBNSh一畢,annveceneeanecnoo,arn,naHbriUisr藝ytofSidThl舒Hbi150080ChiZanoanvers,arn,naHbriNmrlUiiytHbi150080Chirae:eertera
2、osooont,sotness,stronversooontanstronverAbsttThiifmthpihg(y)mthpidg(y)mo·sootnessousea一rezsaees`reznorarevenmhfMilkOlipw牡hOlimgi:sooon;sronversooon;usea一rezsaee;reznorKeywordsmthpittg(y)mthpitMilkOlipOlim.CLCnumber:01773..,·’LetXbeaBanaehspaees(X)betheun
3、itsphereofXandXbeitsdualx任[I}}1〕,,`:S(X)x15saidtobesmoothpointprovidedGar漢(x)={fes(x)x)=x=i}15f(}}}}.singletonx15saidtobestrong(very)smoothpointprovidedx15smoothpointandfor’,,-直ny()x)limply一fo(。)wherestheuniquesup幾)仁s(X人(~}人]I~幾一了岑fi.,-portingfunetionalo
4、fxIt15wellknownsmoothpoint15equivalenttoGateauxdifferen.tiablepointandstrongsmoothpoint15equivalenttoFreehetdifferentiablepoint·,,:etre產(chǎn))stansoranitenonatoeeasurespaeeappingThipl(T藝dffimimAmMT義,,一:0)0)15saidtobeausielakOrliezfunetionifitsatisfies〔co~仁coM
5、·,,u5easuraeoranyuo;i)M()1藝一mblf任[o),·,`,,11)(t)15eonvexvanishingatzeroandthereexistsu0satisfyingotu)M>.一:,It15easytoseethat5alsoausielakOrliezfunetionrite己(ts
6、upu。tu)N1MW)={之M(,,,,:,,,一O}a(t)=supu0(tu)<云t)=supv0tv)一0泛(t)=supv0{之M。}({)N({之N.,,,,,-(tv)7、tv)=(v涼(t))ehaveknownforanyuv0co>0co>W之..,,,uvtu)+N(tv)(teTae)蘭M(·,,,,,,anduv一(tu)+N(tv)iffP一(tu)二vtu)org一(tv)二ug(tv)M三P(蘭eeeveae:Riddt1999一03一29·ounaone:uorteonaaneonanrovFdtiitmSppdbyNFSfChidHilgjigP2應用泛函分6析學報第1卷。,,1id5ttiieediti(〔△iffo)ranylthereexist
8、k>1andaM眾一M>1一`(!’d藝藝measurablenonnegativefunetionhdefinedonTsuehthat{<一d.,,..tut“t,Ml)蘭kM()+h()(t任Tae)(oeenotetesetoaequvaeneeeassesoeasuraereaunetonxByLwdhfll(illf)芝一mbllfi.eneonenearsetdfidTThli。:,Xe`(,一`!“X!,,d才?！?內(nèi)“M,
