Bulletin of Mathematics Vol. 03, No. 01 (2011), pp. 61–68. A UNIFIED PRESENTATION OF SOME CLASSES p-VALENT FUNCTIONS WITH FIXED SECOND NEGATIVE COEFFICIENTS Saibah Siregar Abstract. In this paper we consider the problem involving the unification of some classes of p- valent functions with fixed second negative coefficients. Coefficient inequality, growth and distortion theorems are also determined. 1. INTRODUCTION Let T (p, n) denote the class of functions f of the form: f (z )= z p - ∞  k=p+n a k z k ; a k ≥ 0, p, n ∈ N = {1, 2, 3,...}, (1) which are analytic and p-valent in the unit disk U = {z : z ∈ C;0 < |z | < 1}. Let ST α (p, n) and CT α (p, n) be the subclasses of T (p, n) consisting of p- valently starlike functions of order α and p-valently convex functions of order α, respectively, that is, ST α (p, n)=  f ∈ T (p, n) : Re  zf ′ (z ) f (z )  >α (z ∈ U )  Received 10-12-2010, Accepted 15-12-2010. 2000 Mathematics Subject Classification: 46F20, 52A41 Key words and Phrases: Analytic function, starlike and convex function, unified, growth and distortion 61