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页数:7页
时间:2019-07-09
《无穷远点处亚纯单叶函数的拟Hadamard卷积》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
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
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