Published online by Cambridge University Press: 20 November 2018
Let U be the class of all normalized analytic functions
where z ∈ E = {z : |z| < 1} and ƒ is univalent in E. Let K denote the sub-class of U consisting of those members that map E onto a convex domain. MacGregor [2] showed that if ƒ1 ∈ K and ƒ2 ∈ K and if
1
then F ∉ K when λ is real and 0 < λ < 1, and the radius of univalency and starlikeness for F is .
In this paper, we examine the expression (1) when ƒ1 ∈ K, ƒ2 ∈ K and λ is a complex constant and find the radius of starlikeness for such a linear combination of complex functions with complex coefficients.