Some Properties of q-Convex Functions of Complex Order

Abstract

Let A be the family of functions f(z) which are regular in the open unit disc D = {z : |z| < 1} and satisfy the conditions f(0) = 0, f 0 (0) = 1 for every z ∈ D and let f(z) be an element of A, if f(z) satisfies the condition 1 + 1 b

qz Dq(Dqf(z)) Dqf(z)

≺ 1 + z 1 − qz where b is complex and b 6= 0, then f(z) is called q−convex function of complex order. The class of such functions is denoted by Cq(b). In the present paper we will examine the class of Cq(b).