Boundedness,univalence and quasiconformal extension of Robertson functions |
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Authors: | Ikkei Hotta Li-Mei Wang |
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Institution: | 1.Department of Mathematics,University of Würzburg,Würzburg,Germany;2.Division of Mathematics, Graduate School of Information Sciences,Tohoku University,Sendai, Miyagi,Japan |
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Abstract: | This article contains several results for λ-Robertson functions, i.e., analytic functions f defined on the unit disk ? satisfying f(0) = f′(0) ? 1 = 0 and Re e ?iλ {1 + zf″(z)/f′(z)} > 0 in ? where λ ∈ (?π/2, π/2). We will discuss about conditions for boundedness and quasiconformal extension of Robertson functions. In the last section we provide another proof of univalence for Robertson functions by using the theory of Löwner chains. |
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