参考文献-由算子定义的解析函数的卷积性质

0lf陈建兰1,2,韦叶1,3,刘金林1*(1.vS,225002;2.2Yt-1;zU).Ruscheweyh,NOOR6.sNoor0?,l0I,_:I,_f(z)=f,_(z)*f(z),z/(1-z)+1*f,_(z)=z/(1-z)_,-1,_0.lVI,_f(z)=z+n=2(_)n-1(+1)n-1anzn,(2)()nPochhammer|,l/:()n=(+n)()=1,n=0,0;(+1)(+n-1),nN.T(2)Vw1:z(I,_f(z)=_I,_+1f(z)-(_-1)I,_f(z).(3)!f(z),g(z)U=,iU=fw(z),w(0)=0,|w(z)|0fh(z)Ff.+Y,-1BVfp(z)Ff.p(z)D(V),5Rep(z)2V-1+2(1-V)/(1+|z|).17f(1-z)V=expVln(1-z),V0U=1HqV|V-1|1|V+1|1.28!q(z)U=,f(w),O(w)uDq(z)=OO(w)0,wq(U).7Q(z)=zq(z)O(q(z),h(z)=(q(z)+Q(z).L!1)Q(z)U=;2)Rezh(z)/Q(z)=Re(q(z)/O(q(z)+zQ(z)/Q(z)0,zU.Tp(z)U=,p(0)=q(0),p(U)D,iO(p(z)+zp(z)O(p(z)(q(z)+zq(z)O(q(z)=h(z),5p(z)q(z),iOq(z)Kef.La,b,c(c0,-1,-2,),l+f2F1(a,b;c;z)=1+abcz1!+a(a+1)b(b+1)c(c+1)z22!+.izU,fl,yN+f2F1(a,b;c;z)U=.3La,b,c(c0,-1,-2,),10tb-1(1-t)c-b-1(1-zt)-adt=(b)(c-b)(c)2F1(a,b;c;z),RecReb0,2F1(a,b;c;z)=(1-z)-a2F1a,c-b;c;z/(1-z).1!0W1,W_,-1Bi(_/W)10u(_/W)-12T3-1+2(1-T3)/(1+u)du=1-4(A1-B1)(A2-B2)(1-B1)(1-B2)1-_W10u(_/W)-11+udu.7s_/W10u(_/W)-1/(1+u)du,7c=_/W+1,b=_/W,a=1,z=-1,53_/W10u(_/W)-1/(1+u)du=_W_/W_/W+12F11,_/W;_/W+1;-1=2-12F11,1;_/W+1;2-1.B1=B2=-1H,InffiHq(4)I,_fi(z)=_/Wz1-(_/W)z0t(_/W)-1(1+Ait)/(154y:0lf-t)dt,-1Ai1,i=1,2,5(6)Tp(z)=_/W10t(_/W)-11-(1+A1)(1+A2)+(1+A1)(1+A2)/(1-tz)dt.yN,z-1H,Vp(z)(_/W)10t(_/W)-11-(1+A1)(1+A2)+(1+A1)(1+A2)/(1+t)dt,V7.1.2!_0,0dd,(7)5I,_f(z)/zV(1-z)2V_(1-d)-1=q(z),iOq(z)KDef.7p(z)=I,_f(z)/zV.TH1zp:1+zp(z)/_Vp(z)=I,_+1f(z)/I,_f(z),5(7)T1+zp(z)/_Vp(z)1+(1-2d)z/(1-z).|q(z)=(1-z)2V_(1-d)-1,(w)=1,O(w)=(_Vw)-1,51Vq(z)U=,iOV(w),O(w)2Hq.Q(z)=zq(z)O(q(z)=2(1-d)z/(1-z)U=,iOh(z)=(q(z)+Q(z)=1+(1-2d)z/(1-z),#2Vp(z)q(z),Oq(z)KDef.w1!_0,0d(2-V)-1,iO(2-V)-1.ID:1CHONE,SRIVASTAVAHM.ArgumentestimatesofcertainanalyticfunctionsdefinedbyaclassofmultipliertransformationsJ.MathComputModelling,2003,37:39-49.2LIUJin-lin.CertainintegraloperatorandstronglystarlikefunctionsJ.JMathMathSci,2002,30:569-574.3LIUJin-lin.NotesonJung-Kim-SrivastavaintegraloperatorJ.JMathAnalAppl,2004,294:96-103.4SRIVASTAVAHM,PATELJ.SomesubclassesofmultivalentfunctionsinvolvingacertainlinearoperatorJ.JMathAnalAppl,2005,310:209-228.5,.BL0#M1B=fJ.v:1S,2004,7(2):10-12.6NOORKI.Someclassesofp-valentanalyticfunctionsdefinedbycertainintegraloperatorJ.ApplMath&Comput,2004,157:835-840.7ROBERTSONMS.CertainclassesofstarlikefunctionsJ.MichMath,1985,32:135-140.8MILLERSS,MOCANUPT.OnsomeclassesoffirstorderdifferentialsubordinationJ.MichMath,1985,32:185-195.ConvolutionpropertiesofcertainanalyticfunctionsdefinedbylinearoperatorCHENJian-lan1,2,WEIYe1,3,LIUJin-lin1*(1.CollofMath,YangzhouUniv,Yangzhou225002,China;2.NantongShippingColl,Nantong226006,China;3.DeptofMath&Phys,HuaihaiInstofTech,Lianyungang222005,China)Abstract:MakinguseofalinearoperatorI,_,whichisdefinedherebymeansofaHadamardproduct,theauthorsintroduceanewclassSW,_(A,B)ofcertainnormalizedanalyticfunctionsintheopenunitdisk.Theobjectofthepaperistoderivetheconvolutionpropertiesofthenewclass,andthesubordinationrelatio