Vol. 91, No. 1, 1980

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ISSN: 0030-8730
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 zc1(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