无穷远点处亚纯单叶函数的拟Hadamard卷积

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1、数学杂志Vo1．34(2014)NO．1QUASI—HADAMARDPRoDUCT0FMERoMoRPHICUNIVALENTFUNCT10NSATINFINITYFTANGHuo，一，DENGGuan—tie，LIShu-hai。∞1∑+=一(1．SchoolofMathematicalSciences，BeijingNormalUniversity，Bering100875,，China)(2．SchoolofMathematicsandStatistics，ChifengUniversityCh

2、ifeng024000，China)∞1∑+l一l0nAbstract：Inthispaper，westudyquasi．Hadamardproductproblemforcertainnewsub—nclassesofmeromorphicstarlikeandconvexfunctionsinthepunctureddiskU．BYusingthe—丑amethodofconvolution，wederivesomeresultsassociatedwiththequasi—Hadamardpro

3、ductof0nfunctionsbelongingtothesesubclasses，whichgeneralizessomeknownresults．Keywords：analyticfunctions；meromorphic；starlike；convex；quasi—Hadamardproduct2010MRSubjectClassification：30C45；30C55Documentcode：AArticleID：0255．7797(2014)01．0051—071Introductio

4、nLetEdenotetheclassoffunctionsfoftheformwhichareanalyticinthepunctureddiskU={：0<<1)Alsolet∑denotetheclassoffunctionsoftheform(∈N＼{1))，whichareanalyticinthepunctureddiskU(cf．[1，2])．WhenOLgoestoinfinitythen(n—n)approaches几；henceEa=E．Throughoutthispaper，le

5、tthefunctionsoftheform)=了a0+∑anzn-詈(a0>0，a0，∈N＼{1))，’n=1()=_ao,i+∑。n詈(0o，>0，0，t0，O／∈N＼{1))Receiveddate：2012—04—24Accepteddate：2012—11-05Foundationitem：SupportedbyNationalNaturalScienceFoundationofChinaf112710451；Re-searchFundfortheDoctoralProgramofChina

6、f20100003110004)；NaturalScienceFoundationofInnerMongolia(2010MS0117)andHigherSchoolFoundationofInnerMongolia(NJzc08160)．Biography：TangHuo(1979一)，male，bornatAnqing，Anhui，lecturer，Ph．D．，majorincomplexanalysisandapplication．52JournalofMathematicsVo1．34g(z)

7、了b0+妻n詈(bo>0，b0，∈N＼{1))，n=1andb0ogj(z)+(bo,j>O,bn,y>0】∈Ⅳ＼{1))beregularandunivalentinthepunctureddiskUForthefunctionF∈E，wedefineF(z)=F(z)，F()：F，()+=2，F()=(F())+‘)，andfor南=1，2，⋯，wecanwrite)唧㈤：1+()where∈N＼{1)，0and∈U．Wenotethatwhengoestoo。thenn()approachesn

8、；inthiswaywehave砧I，whichwasintroducedbyFrasinandDarus[3](seealso[4】)．Withthehelpofthediferentialoperator黠，wedefinethefollowingsubclassesofE。．Let∑S(尼，，7)betheclassoffunctionsFdefinedby(1．2)andsatisfyingthecondition(F(z))雎F(z)<礁F(z