Distortion theorems of \beta-spirllike mappings of real order \gamma which have a \Phi-parametric representation in \mathbb {C}^{n} ^{*}

• Yu, Fang ^[1] ; Zeng, Luyi ^[1] ; Xiong, Liangpeng ^[1]
  1. [1] Jiangxi Science and Technology Normal University

     Jiangxi Science and Technology Normal University

     China

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 77, Fasc. 3, 2026, págs. 749-764
• Idioma: inglés
• DOI: 10.1007/s13348-025-00489-5
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let \gamma \in (0,1], \beta \in (-\frac{\pi }{2}, \frac{\pi }{2}) and \Phi be a holomorphic function such that \Phi (0)=1 and \Re (\Phi (\zeta ))>0 on the open unit disk in \mathbb {C}. A class of \beta-spirllike mappings f of real order \gamma on the unit ball \mathbb {B_{X}} in a complex Banach space \mathbb {X} is defined, which has a \Phi-parametric representation and satisfies that x=0 is zero of order k+1 of f(x)-x. Kinds of versions of sharp distortion results are established over this class. Our works extend the distortion theorem of holomorphic functions in \mathbb {C} to the case in \mathbb {X}.

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