An investigation on a subclass of p-valently starlike functions in the unit disc

Abstract

Let A(p) denote the class of functions of the form f(z) = z(p) +a(p+1)z(p+1)+a(p+2)z(p+2) +... which are regular and p-valent in the open unit disc D = {z : vertical bar z vertical bar < 1}. Let M-p(alpha) be the subclass of A(p) consisting of functions f(z) which satisfy Re(zf'(x)/f(z)) < alpha, (z is an element of D) for some real alpha (alpha > 1).

The aim of this paper is to give a representation theorem, a distortion theorem and a coefficient inequality for the class M-p(alpha).