New Integral Operator for Analytic Functions

Let Apn be the class of functions fz given by fz=zp+ap+nzp+n+ap+n+1zp+n+1+MIDLINE HORIZONTAL ELLIPSIS which are analytic in the open unit disk U. For fz is an element of Apn, new integral operators O-jfz and Ojfzj=0,1,2,MIDLINE HORIZONTAL ELLIPSIS. are considered. The operators O-jfz and Ojfz satisfy OjO-jfz=O-jOjfz=fz and O-j*Ojfz=Oj*O-jfz=f*fz for the convolution * of O-jfz and Ojfz. In the present paper, the dominants for both operators O-jfz and Ojfz and subordinations for O-jfz and Ojfz are discussed. Also, new subclass Tp gamma m,delta,rho;m,j concerning with m different boundary points is defined and discussed. Moreover, some interesting problems of Tp gamma m,delta,rho;m,j associated with Ojfz are obtained. Furthermore, some interesting examples for our results are considered.