Radius problems associated with pre-Schwarzian and Schwarzian derivatives
Abstract
Some of important univalence criteria for a non-constant meromorphic function f(z) on the unit disk involve its pre-Schwarzian or Schwarzian derivative. We consider an appropriate norm for the pre-Schwarzian derivative, and discuss the problem of finding the largest possible r∈ (0,1) for which the pre-Schwarzian norm of the dilation r-1f(rz) is not greater than a prescribed number for normalized univalent functions f(z) in the unit disk. Similar results concerning the Schwarzian derivative are also obtained
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