The Koebe Domain for Concave Univalent Functions
2000 Mathematics Subject Classification: 30C25, 30C45. K is the exact Koebe domain for the class of functions considered here.
Concave functions, Blaschke products, and polygonal mappings.
An extremal problem for polynomials with a prescribed value at a given point of the real axis.
A proof of the Livingston conjecture for the fourth and the fifth coefficient of concave univalent functions
Let D denote the open unit disc and f:D → ℂ̅ be meromorphic and injective in D. We further assume that f has a simple pole at the point p ∈ (0,1) and an expansion , |z| < p. In particular, we consider f that map D onto a domain whose complement with respect to ℂ̅ is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of these functions is denoted by Co(p). It is proved that for p ∈ (0,1) the domain of variability of the coefficient...
A sharp bound for the Schwarzian derivative of concave functions
We derive a sharp bound for the modulus of the Schwarzian derivative of concave univalent functions with opening angle at infinity less than or equal to πα, α ∈ [1,2].
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