Boundedness, univalence and quasiconformal extension of Robertson functions

Article

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{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.

Key words

Robertson function spirallike function univalent function quasiconformal mapping Löwner (Loewner) chain 

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Copyright information

© The Indian National Science Academy 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WürzburgWürzburgGermany
  2. 2.Division of Mathematics, Graduate School of Information SciencesTohoku UniversitySendai, MiyagiJapan

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