The Fekete and Szegő Problem for a Class of Holomorphic Mappings Associated with Starlike Mappings on the Unit Balls of Complex Banach Spaces

Abstract

In this paper, we first establish a refinement of the coefficient inequality for subordinate functions on the unit disc $\mathbb{U}$ in $\mathbb{C}$. Next, as applications of this inequality, we will obtain some refinements of the Fekete and Szegő inequalities for a class of holomorphic mappings associated with starlike mappings and quasi-convex mappings of type B on the unit ball $\mathbb{B}$ of a complex Banach space. The results presented here would generalize and improve some recent works of several authors [12, 20, 23].

Keywords

Fekete and Szegő problem / starlike mapping / quasi-convex mappings / subordination