Some refinements of the Fekete and Szegö inequalities for a class of holomorphic mappings associated with quasi-convex mappings

• Xu, Qinghua ^[1] ; Jiang, Ting ^[1]
  1. [1] Zhejiang University of Science and Technology

     Zhejiang University of Science and Technology

     China

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 77, Fasc. 1, 2026, págs. 85-97
• Idioma: inglés
• DOI: 10.1007/s13348-024-00457-5
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let E be the unit ball of a complex Banach space, \mathcal {M}_g(E) be a class of holomorphic mappings on E (see Definition 1.2). Let F be a holomorphic mapping on E, and have the power series expansion F(x)=x+\sum \limits _{l=k+1}^{\infty }\frac{D^{l}F(0)(x^{l})}{l!} for x near the origin, where k is a positive integer. In this paper, we establish various Fekete and Szegö inequalities for F such that F is locally biholomorphic on E and (DF(x))^{-1}(D^2F(x)(x^2)+DF(x)(x))\in \mathcal {M}_g(E). The results presented here generalize some known results in [10, 21] and [24].

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