Some results of quasi-convex mappings which have a Φ-parametric representation in higher dimensions

被引：0

作者：

Xiong, Liangpeng ^{[1
]}

Xiong, Junzhou ^{[1
]}

Zhang, Ruyu ^{[1
]}

机构：

[1] Jiangxi Sci & Technol Normal Univ, Sch Math & Comp Sci, Nanchang 330038, Jiangxi, Peoples R China

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2024年 / 14卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Fekete-Szego inequalities; Homogeneous expansions; Phi-parametric representation mappings; k-Fold symmetric mapping; Quasi-convex mappings; SZEGO PROBLEM; FEKETE; CONJECTURE; SUBCLASS; STARLIKE; PROOF;

D O I：

10.1007/s13324-024-00930-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let E-X be a unit ball on complex Banach space X and Phi be a convex function such that Phi(0)=1 and R Phi(xi) > 0 on D = {z is an element of C : |z| < 1}. In this paper, we continue the work related to the class Q(B)(Phi)(EX)of quasi-convex mappings of type B which have a Phi-parametric representation on E-X, where the mappings f is an element of Q(B)(Phi)(E-X) are k-fold symmetric, k is an element of N. We give the improved Fekete-Szego inequalities for the class Q(B)(Phi)(E-X)and establish the sharp bounds of all terms of homogeneous polynomial expansions for some subclasses of Q(B)(Phi)(E-X). Our main results are closely related to the Bieberbach conjecture in higher dimensions.

引用

页数：20

共 34 条

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[2]

Cartan H., 1933, Lecons sur les Fonctions Univalentes ou Multivalentes

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