|
|
|
|
|
The radius of
starlikeness for a class of regular functions defined by an
integral
V. Karunakaran and Michael Robert Ziegler |
|
Vol. 91 (1980), No. 1, 145–151
|
Abstract |
|
Let F(z), f(z), and g(z) be regular in the unit disc E = {z : z < 1}, be normalized by F(0) = f(0) = g(0) = 0 and F′(0) = f′(0) = g′(0) = 1, and satisfy the equation zc−1(c + 1)f(z) = [F(z)g(z)c]′, c ≧ 0. This paper is concerned with studying relationships between the mapping properties of these functions. The principle result is the determination of the radius of β-starlikeness of f(z) when F(z) and g(z) are restricted to certain classes of univalent starlike functions. Conversely, a lower bound for the radius of β-starlikeness of F(z) is obtained when f(z) and g(z) satisfy similar conditions. |
Mathematical Subject Classification 2000
Primary: 30C45
|
Milestones
Received: 27 June 1977
Revised: 7 February 1978
Published: 1 November 1980
|
Authors |
| V. Karunakaran | |
| Michael Robert Ziegler | |
|
