Convex Functions and the Nehari Un 1 Valence Criterion
نویسنده
چکیده
f " ' f " 2 where Sf := (p-) 1⁄2 (iv) denotes the Schwarzian derivative, and that this result is sharp, as the function f(z) = 1⁄2 log 11 z + z shows. Tile method of the proof does not give all sharp functions. We shall show that the sharp function is essentially unique using another approach implying Nehari's result. This shows furthermore that all convex domains except of parallel strip domains are Jordan domains in £, using a result of Gehring and Pommerenke [3]. Moreover we give a geometrical description of convex domains whose corresponding convex functions satisfy the stronger relation
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