Coefficient inequality for q-starlike functions

Abstract

Let A be the class of analytic functions f which are regular and satisfying the conditions f (0) = 0, f'(0) = 1. In other words each f in A has the power series representation f(z) = z + a(2)z(2) + a(3)z(3) + ... in the open unit disc D = {z parallel to z} < 1}. For every q is an element of (0, 1), let q-difference operator be defined as follows

D(q)f(z) = f(z) - f(zq)/z(1-q) (z is an element of D)

Making use of the above operator we define a class of analytic functions, so called q-close-to-convex function with respect to Janowski starlike functions and the class of such functions is defined by K-q(A, B). In the present paper we will study on this class. (C) 2015 Elsevier Inc. All rights reserved.