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

Qinghua Xu , Xiaohua Yang , Taishun Liu

Frontiers of Mathematics ›› : 1 -14.

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Frontiers of Mathematics ›› : 1 -14. DOI: 10.1007/s11464-022-0309-6
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The Fekete and Szegő Problem for a Class of Holomorphic Mappings Associated with Starlike Mappings on the Unit Balls of Complex Banach Spaces

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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].

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

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Qinghua Xu, Xiaohua Yang, Taishun Liu. The Fekete and Szegő Problem for a Class of Holomorphic Mappings Associated with Starlike Mappings on the Unit Balls of Complex Banach Spaces. Frontiers of Mathematics 1-14 DOI:10.1007/s11464-022-0309-6

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