Research Information System
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, no.2, pp.249-253, 2012 (ESCI)
Let f(z) = a(1)z + a(1)z(2) +... , a(1) not equal 0, be regular in vertical bar z vertical bar < 1 and have there no zeros except at the origin. Reade ([3]) and the Sakaguchi ([2]) showed that a necessary and sufficient condition for f(z) to be a member of the class C(k) is that f(z) has a representation of the form f(z) = s(z)(p(z))(k) where s(z) is a regular function starlike with respect to the origin for vertical bar z vertical bar < 1, k is a positive constant, and p(z) is a regular function with positive real part in broken vertical bar z broken vertical bar< 1. The class of closetostar functions introduced by Reade ([4]) is equivalent to C(1). In this paper we define the class C(k, A, B) (-1 <= B <= A <= 1, k is positive constant) which contains the functions of the form f(z) = s(z) (p(z))(k) where s(z) is a regular Janowski starlike function, and p(z) is a regular function with positive real part in vertical bar z vertical bar < 1. The aim of this paper is to give some properties and distortion theorems for this class.