Boundedness, univalence and quasiconformal extension of Robertson functions

Ikkei Hotta () and Li-Mei Wang ()
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Ikkei Hotta: University of Würzburg
Li-Mei Wang: University of Würzburg

Indian Journal of Pure and Applied Mathematics, 2011, vol. 42, issue 4, 239-248

Abstract: Abstract This article contains several results for λ-Robertson functions, i.e., analytic functions f defined on the unit disk ⅅ satisfying f(0) = f′(0) − 1 = 0 and Re e −iλ {1 + zf″(z)/f′(z)} > 0 in ⅅ 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.

Keywords: Robertson function; spirallike function; univalent function; quasiconformal mapping; Löwner (Loewner) chain (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s13226-011-0016-6

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