• 제목/요약/키워드: Schwarzian derivatives

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STARLIKENESS AND SCHWARZIAN DERIVATIVES OF HIGHER ORDER OF ANALYTIC FUNCTIONS

  • Kwon, Ohsang;Sim, Youngjae
    • 대한수학회논문집
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    • 제32권1호
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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.

Some properties of the set of schwarzians of conformal functions

  • Jong Su An;Tai Sung Song
    • 대한수학회논문집
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    • 제11권3호
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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.

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