NEW SUBCLASS OF STARLIKE FUNCTIONS OF COMPLEX ORDER

The aim of the present paper is to investigate a new subclass of starlike functions of complex order, b not equal 0. Let f(z) = z + a2z^2 +… be an analytic function in the unit disc D = {z| |z| < 1} which satisfies 1 + 1/ b (z f’(x/f(x-1))=1+Aw(x)/ 1+Aw(x) for some w element of (ohm) Then f is called a Janowski starlike function of complex order b, where A and B are complex numbers such that Re(1 - AB) ≥|A-B|, im(1- AB ) <|A- B|,|Bj < 1, and w(z) is a Schwarz function in the unit disc D [1], [10], [12]. The class of these functions is denoted by S*(A;B; b). In this paper we will give the representation theorem, distortion theorem, two point distortion theorem, Koebe domain under the montel normalization, and coefficient inequality for this class.