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<p>This paper studies a class of Koebe-type harmonic quasiconformalfunctions. It is motivated by the shear construction of Clunie and Sheil-Small[Ann. Acad. Sci. Fenn. Ser. A I Math., 9 (1984), 3–25] and the harmonic quasiconformalKoebe function. Equivalent univalence conditions, pre-Schwarzian andSchwarzian norms, coefficient inequalities, as well as growth and area theorems forthis family of functions are established. These findings improve several previouslyknown results.</p>

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On Koebe-type functions for harmonic quasiconformal mappings

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Z.-G. Wang,
  • J.-L. Qiu,
  • A. Rasila

摘要

This paper studies a class of Koebe-type harmonic quasiconformalfunctions. It is motivated by the shear construction of Clunie and Sheil-Small[Ann. Acad. Sci. Fenn. Ser. A I Math., 9 (1984), 3–25] and the harmonic quasiconformalKoebe function. Equivalent univalence conditions, pre-Schwarzian andSchwarzian norms, coefficient inequalities, as well as growth and area theorems forthis family of functions are established. These findings improve several previouslyknown results.