Vol. 61, No. 1, 1975

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Certain classes of regular univalent functions

V. Karunakaran

Vol. 61 (1975), No. 1, 173–182
Abstract

If f(z) and g(z) are starlike functions of orders α and γ for α,γ [0,1), then it is shown that

           ∫
-2--  z
F (z) = g(z)  0 f(t) dt

is β-starlike for |z| < δ, where δ is a function of α, β, γ. Conversely, a sharp estimate is obtained for the radius of β-starlikeness of the class of functions

f(z) = 2−1(g(z)F (z))′,

where g(z) and F(z) are starlike functions of orders γ and α respectively, with α + γ 1.

Mathematical Subject Classification
Primary: 30A32, 30A32
Milestones
Received: 14 April 1975
Revised: 22 July 1975
Published: 1 November 1975
Authors
V. Karunakaran