Hyperbolically 1-convex functions

William Ma; David Minda; Diego Mejia

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Hyperbolically convex functions

Wancang Ma, David Minda (1994)

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We investigate univalent holomorphic functions f defined on the unit disk 𝔻 such that f(𝔻) is a hyperbolically convex subset of 𝔻; there are a number of analogies with the classical theory of (euclidean) convex univalent functions. A subregion Ω of 𝔻 is called hyperbolically convex (relative to hyperbolic geometry on 𝔻) if for all points a,b in Ω the arc of the hyperbolic geodesic in 𝔻 connecting a and b (the arc of the circle joining a and b which is orthogonal to the unit circle)...

A Subclass Of Close-To-Convex Functions

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Certain Applications of Differential Subordination

K. S. Padmanabhan, R. Manjini (1986)

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Convex combination of analytic functions

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Open Mathematics

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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).