Coefficient inequality for q-starlike functions

摘要

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+a2z2+a3z3+⋯ in the open unit disc D={z||z|<1}. For every q ∈ (0, 1), let q-difference operator be defined as follows Dqf(z)=f(z)−f(qz)z(1−q)(z∈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 Kq(A, B). In the present paper we will study on this class.