Multivalued starlike functions of complex order
Abstract
Let S
∗
λ
(1−b)(b 6= 0, complex) denote the class of functions f(z) =
z+a2z
2+· · · analytic in the open unit disc D = {z ∈ C||z| < 1} which
satisfy for z = reiθ ∈ D,
f(z)
z
6= 0 and Re ·
1 + 1
b
µ
z
(Dλ
f(z))′
D
λ
f(z)
− 1
¶¸ >
0 (0 ≤ λ < 1), where Dλ
f(z) = Γ(2 − λ)z
λD
λ
z
f(z) and Dλ
z
f(z) is the
fractional derivative of f(z).
The aim of this paper is to investigate certain properties of the
mentioned above class.
Subject
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