多叶解析函数族子类的一些结果.pdf

《多叶解析函数族子类的一些结果.pdf》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．4S0MERESULTSFoRCERTAINSUBCLASS0F=0pMULTIVALENTANDANAITICFUNCTIoNSp～XIONGLiang—peng，HANHong-wei，MAZhi—yuan∞∑0(SchoolofEngineering0ndTechnical，ChengDuUniversityofTechnDlogy，Lesh。n6140n07,Chin0)+Pn+Abstract：Inthispaper，weinvestigatefunctionsoftheclassG；，ca，b，)whichpareanal

2、yticandmultivalentintheopenunitdiskU={z：lZl<1)．Byusingthemethodoffunctiontheory，weobtainsomegeneralresultsconcerningthequasi—HadamardproductandtheextremepointsandsupportpointsofG；，c(0，b，)．Manyinterestingconsequencesofthemainresultsextendrelatedworksofseveralearlierauthors．Keywords：analyti

3、cfunctions；multivalentfunction；quasi—Hadamardproduct；extremepoints；supportpoints2010MRSubjectClassification：30C45ⅡDocumentcode：AArticleID：0255—7797(2014)O4—0651—111Introduction∞∑LetAdenotethefunctionsz)oftheform(ap>0；an+p≥0；p∈N={1，2，⋯))whicharemultivalentandanalyticintheunitdiscU=z∈c：IZl<

4、1}．Here，wedefinethegeneralquasi—Hadamardproductofthefunctions，by一一=垂i~an+p,i，(1．2)where)(areanynonnegativerealnumbersand，t()∈Aaredefinedas(1．1)，i=1，2，⋯，s．AfunctionL(z)definedby(1．1)issaidtobeintheclassG；(n，b，)ifandonlyif一(z)<∈apReceiveddate：2013—01—24Accepteddate：2013．06．09Foundationitem：

5、SupportedbyScientificResearchFundofSichuanProvincialEducationDe-partment(14ZB0364)．Biography：XiongLiangpeng(1983一)，male，bornatWuhan，Hubei，lecture，majoringeometricfunctiontheory．E—mail：xlpwxf@163．com．652JournalofMathematicsV0l_34where一1≤a

6、()suchthatisinthec1assG6，)WealsohavethefollowingspecialcasesonG(n，b，)anda，b，)：(I)Forap三1in(1．1)，theclassesG；(0，b，)三a，b，)and^a，b，)三a，b，)werestudiedbyRaina，Nahar[1】．(II)ForP=1，a=一1，b=OL，=，theclassesGi(一1，，)三So(，)andA(一1，O／，)三Co(，)introducedbyOwaf21arewellknown．Usingsimilarargumentsasgivenby

7、Raina，Nahar[1]jwecaneasilyprovethefollowingLemmasforfunctionsintheclassesGa，b，)anda，b，盯)：Lemma1．1Afunctionz)definedby(1．1)belongstoG(0，b，)ifandonlyif∑{(1+6cr)n+(6一。)p+≤(6一。)p口p，(1．4)n=1where一1≤b