Some convolution properties of a certain class of p-valent analytic functions

Let A(p) denote the class of functions f (z) = z(p) +Sigma(infinity)(n=p+1) a(n)z(n) (p is an element of N = (1,2,...)) which are analytic and p-valent in the unit disc U = {z : vertical bar z vertical bar < 1}. The objective of the present work is to obtain some convolution properties for the class P(p,alpha) = {f(z) is an element of A(p) : Re{f'(z)/z(p-1)} > alpha, 0 <= alpha < p, p is an element of N, z is an element of U}. Also we prove that the integral operator integral(p,c)(f) is an element of P(p,beta)(f(z) is an element of A(p)), where the value beta is sharp. (C) 2008 Elsevier Ltd. All rights reserved.