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

摘要

Let A(p), p is an element of N, be the class of functions f(z) = z(p) + a(p+1) z(p+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 I(n+p-1)f = f(n+p-1)((-1)) * f such that (f(n+p-1)((-1)) * f(n+p-1)) (z) = z(p)/1-z, where f(n+p-1)(z) = z(p)/(1-z)(n+p) and * denotes convolution or Hadamard product. Using this integral operator, a new subclass S-n(p, alpha) of A(p), 0 less than or equal to alpha < p is introduced in E and some interesting properties of this class are investigated. (C) 2003 Elsevier Inc. All rights reserved.