Certain classes of regular univalent functions

V. Karunakaran

Vol. 61 (1975), No. 1, 173–182

DOI: 10.2140/pjm.1975.61.173

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

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

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