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Boundedness, univalence and quasiconformal extension of Robertson functions

Author

Listed:
  • Ikkei Hotta

    (University of Würzburg
    Tohoku University)

  • Li-Mei Wang

    (University of Würzburg
    Tohoku University)

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.

Suggested Citation

  • Ikkei Hotta & Li-Mei Wang, 2011. "Boundedness, univalence and quasiconformal extension of Robertson functions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(4), pages 239-248, August.
    • Handle: RePEc:spr:indpam:v:42:y:2011:i:4:d:10.1007_s13226-011-0016-6
    DOI: 10.1007/s13226-011-0016-6
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