• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.93-106
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• 2017

In this paper we apply the third-order differential subordination results to normalized analytic functions in the open unit disk. We obtain appropriate classes of admissible functions and find some sufficient conditions of functions to be starlike associated with Tamanoi's Schwarzian derivative of third order. Several interesting examples are also discussed.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1661-1676
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• 2008

Norm estimates of the pre-Schwarzian derivatives are given for meromorphic functions in the outside of the unit circle. We deduce several univalence criteria for meromorphic functions from those estimates.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.665-672
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• 1996

Let U denote the set of all Schwarzian derivatives $S_f$ of conformal function f in the unit disk D. We show that if $S_f$ is a local extreme point of U, then f cannot omit an open set. We also show that if $S_f \in U$ is an extreme point of the closed convex hull $\bar{co}U$ of U, then f cannot omit a set of positive area. The proof of this uses Nguyen's theorem.