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Convex combination of analytic functions

Nak Eun Cho, Naveen Kumar Jain, V. Ravichandran (2017)

Open Mathematics

Radii of convexity, starlikeness, lemniscate starlikeness and close-to-convexity are determined for the convex combination of the identity map and a normalized convex function F given by f(z) = α z+(1−α)F(z).

Convex meromorphic mappings

Albert E. Livingston (1994)

Annales Polonici Mathematici

We study functions f(z) which are meromorphic and univalent in the unit disk with a simple pole at z = p, 0 < p < 1, and which map the unit disk onto a domain whose complement is either convex or is starlike with respect to a point w₀ ≠ 0.

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