Geodesic
Linear Combinations of Univalent Functions with Complex Coefficients
Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 712-717

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Stump, Robert K. Linear Combinations of Univalent Functions with Complex Coefficients. Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 712-717. doi: 10.4153/CJM-1971-080-6
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[4] 4. Strohhäcker, E., Beitrage zur Théorie der schlichte Funktionen, Math. Z. 37 (1933). 356–380. Google Scholar

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