Journal of the Vol. 35, pp. 400-407, 2016 Nigerian Mathematical Society c Nigerian Mathematical Society A GENERALIZATION OF A STARLIKENESS CONDITION C. N. EJIEJI 1 AND K. O. BABALOLA In this paper, we prove a generalization of a well known starlike- ness condition in the unit disk using a method of linear combi- nations of certain geometric expressions. Some interesting corol- laries are mentioned. Keywords and phrases: Analytic and univalent functions, star- like functions, univalence condition, Caratheodory functions. 2010 Mathematical Subject Classification: 30C45, 30C50. 1. INTRODUCTION Let A denote the class of functions: f (z)= z + a 2 z 2 + ··· which are analytic in the open unit disk E = {z ∈ C : |z| < 1}. A function f ∈ A is called starlike if and only if f maps E onto a starlike domain and it is well known that such f satisfy the necessary and sufficient condition: Re zf ′ (z) f (z) > 0. (1) In [2] the author introduced subclasses S σ n of starlike functions sat- isfying Re L σ n+1 f (z) L σ n f (z) > σ - (n + 1) σ - n , σ ≥ n +1, n ∈ N (2) using the convolution operators L σ n : A → A defined as follows: L σ n f (z)=(τ σ ∗ τ (-1) σ,n ∗ f )(z) where ∗ denote the convolution of f ∗ g defined as (f ∗ g )(z)= z + ∞  k=2 a k b k z k Received by the editors September 03, 2014; Revised: February 26, 2016; Accepted: July 21, 2016 DOI: 1 Corresponding author 400