Some classes of p-valent analytic functions defined by certain integral operator

摘要

Let A(p), p∈N, be the class of functions f(z)=zp+ap+1zp+1+⋯, analytic in the open unit disc E. For n=0,1,2,…,n>−p, a certain integral operator In+p−1:A(p)→A(p) is defined as In+p−1f=f(−1)n+p−1★f such that (f(−1)n+p−1★fn+p−1)(z)=zp1−z, where fn+p−1(z)=zp(1−z)n+p and ★ denotes convolution or Hadamard product. Using this integral operator, a new subclass Sn(p,α) of A(p), 0⩽α